Jan

01/06/09
Laurent Damanet  Stanford University
Compressive Wave Computation
AbstractThis talk presents a strategy for computational wave propagation that
consists in decomposing the solution wavefield onto a largely incomplete set of
eigenfunctions of the weighted Laplacian, with eigenvalues chosen randomly. The
recovery method is the ell1 minimization of compressed sensing. For the
mathematician, we establish three possibly new estimates for the wave equation
that guarantee accuracy of the numerical method in one spatial dimension. For
the engineer, the compressive strategy offers a unique combination of
parallelism and memory savings that should be of particular relevance to
applications in reflection seismology. Joint work with Gabriel Peyre. 
01/08/09
Dan Rogalski  UCSD
Organizational Meeting

01/08/09
Andre Minor  UCSD
Question: Who put what? In where?!?
AbstractAnswer: Kodaira put a compact Hodge manifold in
projective space.
We will spend an hour building up to the statement of the Kodaira
embedding theorem. Any graduate student should feel welcome as we will
build up the basic background material necessary to understand the
statement of the theorem. If time permits, we will present a *very*
brief outline of how a proof might
look and some applications. See you there. 
01/08/09
Cristian Popescu  UCSD
Organizational Meeting

01/08/09
Enno Lenzmann  Massachusetts Institute of Technology
Nonlinear Evolution Equations and Gravitational Collapse
Abstract\noindent In this talk, I will discuss a novel class of nonlinear dispersive equations, which describe the dynamical evolution of selfgravitating relativistic matter. In fact, the analysis of these model equations will give a mathematical vindication of Chandrasekhar's acclaimed physical theory of gravitational collapse. In particular, I will present results concerning the wellposedness of the initialvalue problem, the singularity formation of solutions (blowup), as well as solitary wave solutions and their stability. Time permitting, I will also discuss some recent and ongoing work. \\
\noindent This is partly joint work with J\"urg Fr\""ohlich (ETH Z\""urich)

01/12/09
Jason P. Bell  Simon Fraser University
A transcendence degree for division algebras

01/13/09
Justin Roberts  UCSD
Morse theory  Organizational meeting
AbstractThis term's topology seminar will be on Morse theory and its applications.
We'll look first at the basic idea of gradient flow on finitedimensional manifolds, and how this gives us cell and handle decompositions. Then we'll look at the original applications, to geodesics on Riemannian manifolds and to Bott periodicity. Finally we'll look at more modern developments, including perhaps the Morse category of a manifold, Fukaya's approach to the cup product and Massey products, Floer homology, circlevalued Morse theory and combinatorial Morse theory.\\\noindent As usual this is a learning seminar, where the volunteering participants give talks. At the first meeting I'll give an overview lecture and we'll try to arrange speakers for the rest of term.

01/13/09
Sami Assaf  Massachusetts Institute of Technology
Affine dual equivalence and kSchur positivity.
AbstractIn this talk, we present an analog of dual equivalence for
affine permutations. Exploiting the connection between affine
permutations and ncores, this establishes the Schur positivity of the
strong Schur functions introduced by Lam, Lapointe, Morse and Shimozono,
which are generalizations of the kSchur functions introduced by
Lapointe, Lascoux and Morse. Time permitting, we will show how this
approach may ultimately lead to an explicit connection between Macdonald
polynomials (and, more generally, LLT polynomials) and kSchur
functions. \\\noindent This is joint work with Sara Billey at the University of Washington.

01/14/09
Evgeny Khukhro  Univ. of Manchester and Novosibirsk Inst. of Math.
Groups and Lie Algebras with almost regular automorphisms

01/14/09
Neil Donaldson  UC Irvine
Isothermic submanifolds in Euclidean space
AbstractWe give a positive answer to Burstall's question of whether there exists an interesting theory of isothermic submanifolds of dimension $>2$ in $R^n$. We relate chains of such manifolds to solutions of a system of PDEs and describe their moduli space. We also describe Christoffel and Darboux/Ribaucour transforms of isothermic chains.

01/15/09
Dan Rogalski  UCSD
An introduction to central simple algebras and the Brauer group

01/15/09
Mary Radcliffe  UCSD
Jug Problems and Algorithms
AbstractAs seen in \textit{Die Hard with A Vengeance}, we investigate the classic puzzle of making 4 gallons using only a 3 and a 5gallon jug. We'll look at various generalizations of this puzzle, when and how they are solvable, and how quickly one can arrive at a solution.

01/15/09
Michael Volpato  UCSD
Counting superspecial abelian varieties
AbstractBy invoking a result originally due to G. Shimura, we give a new proof
of a generalization of a theorem of Deuring concerning supersingular
elliptic curves, namely, a mass formula for superspecial abelian
varieties with PELstructures in characteristic p. This mass formula
is then applied to estimate the dimension of Siegel modular cusp
spaces modulo p and count the number of irreducible components in the
supersingular region of the Siegel modular variety. 
01/15/09
Gil Ariel  University of Texas, Austin
Modeling and computation with multiple time scales
Abstract\noindent Many interesting examples of dynamical systems involve several well separated time scales. In many applications, for example in molecular dynamics simulations, one is only interested in the slow aspects of dynamics, or on the longtime behavior of the solutions. However, when the different scales are coupled, small or fast perturbations can build up to an observable effect that cannot be neglected. \\
\noindent In this talk I will discuss several types of models and address some of the analytic and computational difficulties common to many systems evolving on multiple time scales. We give a complete characterization of the slow aspects of the dynamics and devise efficient computational algorithms that take advantage of the scale separation. It is shown that the computational cost is practically independent of the spectral gap. Among the systems studied are highly oscillatory ODEs and a benchmark model of elastic spheres with disparate masses.

01/16/09
Ronny Hadani  University of Chicago
Group representation patterns in digital signal processing I
Abstract\noindent In my colloquium talk, I will explain how various fundamental structures from group representation theory appear naturally in the context of discrete harmonic analysis and can be applied to solve concrete problems from digital signal processing. I will begin by describing our solution to the problem of finding a canonical orthonormal basis of eigenfunctions of the discrete Fourier transform (DFT). Then I will explain how to generalize the construction to obtain a larger collection of functions that we call "The oscillator dictionary". Functions in the oscillator dictionary admit many interesting properties, in particular, I will explain two of these properties which arise in the context of problems of current interest in communication theory. This is joint work with Shamgar Gurevich (Berkeley) and Nir Sochen (Tel Aviv). \\
\noindent There is a sequel to my colloquium talk, which will be slightly more specialized and will take place during the algebraic geometry seminar. Here, my main objective is to introduce the geometric Weil representation which is an algebrageometric ($ \ell $adic Weil sheaf) counterpart of the Weil representation. Then, I will explain how the geometric Weil representation is used to prove to main result stated in my colloquium talk. In the course, I will explain Grothendieck's geometrization procedure by which sets are replaced by algebraic varieties and functions by sheaf theoretic objects.

01/16/09
Ronny Hadani  University of Chicago
Group representation patterns in digital signal processing II: the geometric Weil representation
AbstractThis talk is a sequel to my colloquium talk, given earlier in the day. My main objective is to introduce the geometric Weil representation which is an algebrageometric
(ladic Weil sheaf) counterpart of the Weil representation. Then, I will
explain how the geometric Weil representation is used to prove to main
result stated in my colloquium talk. In the course, I will explain
Grothendieck's geometrization procedure by which sets are replaced by
algebraic varieties and functions by sheaf theoretic objects. 
01/20/09
Justin Roberts  UCSD
Classical Morse theory

01/20/09
ChingShan Chou  University of California, Irvine
Computation and Cell Signaling
AbstractMy talk is composed of three parts. The first part is on high order
residual distribution (RD) schemes for steady state hyperbolic
conservation laws. High order RD schemes are conservative schemes that
overcome the restriction of mesh sizes in high order finite difference
schemes, and yet have comparable computational costs. It has a broad
range of applications from NavierStokes equations to semiconductor
simulations. I will present the design of the scheme, a LaxWendroff
type theorem and the numerical results. In the second part, I will
discuss the applications in systems biology. The modeling of the two
biological systemscell polarization and multistage cell lineages,
and the computational aspect will be discussed. New efficient
numerical schemes for both time evolution and steady state
reactiondiffusion equations that arise in many biological models will
be presented in the third part. 
01/20/09
Karin Baur  ETH Zurich
Representation Theory Seminar
AbstractConsider a parabolic subgroup of a reductive group G. By a theorem of Richardson (1974), the adjoint action of P on its nilpotent radical has an open dense orbit.
In general, there is an infinite family of orbits, so the description of the Porbits is a ``wild'' problem.In type A there exists a translation of this problem into a question of representationtype of a category of representations of an algebra due to Hille and R\"ohrle (1999). In this talk I will describe their approach and explain how it can be extended to deal with parabolic subgroups of orthognal groups. 
01/20/09
Sophie Chen  Berkeley and Institute for Advanced Study
Optimal curvature decays, asymptotically flat manifolds and elliptic systems

01/20/09
Paul Horn  UCSD
Random Subgraphs of a Given Graph
AbstractData from realworld graphs often contains incomplete information, so we
only observe subgraphs of these graphs. It is therefore desirable to
understand how a typical subgraph relates to the underlying host graph.
We consider several interrelated problems on both random trees and
random subgraphs obtained by taking edges of the host graph
independently with probability $p$. In the second case, we study the
emergence of the giant component. We also use the spectral gap to
understand discrepancy and expansion properties of a random subgraph.
The Erd\H{o}sR\'enyi random graph is the special case of this where the
host graph is the complete graph $K_n$. Additional applications include
taking a contact graph as the host graph, and viewing random subgraphs
as outbreaks of a disease. 
01/20/09
HsianHua Tseng  University of Wisconsin
Recent progress in GromovWitten theory of DeligneMumford stacks
Abstractt has been over two decades since M. Gromov initiated the study
of pseudoholomorphic curves in symplectic manifolds. In the past decade
we have witnessed mathematical constructions of GromovWitten theory for
algebraic varieties, as well as many major advances in understanding their
properties. Recent works in string theory have motivated us to extend our
interests to GromovWitten theory for DeligneMumford stacks. Such a
theory has been constructed, but many of its properties remain to be
understood. In this talk I will explain the main ingredients of
GromovWitten theory of DeligneMumford stacks, and I will discuss some
recent progress regarding main questions in GromovWitten theory of
DeligneMumford stacks. 
01/21/09
William Stein  Univ. of Washington, Project Founder and Director
Introduction to Sage

01/21/09
Reza Seyyedali  Johns Hopkins University
Balanced Metrics and Chow Stability of Ruled Manifolds
AbstractIn 1980, I. Morrison proved that slope stability of a vector bundle of rank 2 over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. Using the notion of balanced metrics and recent work of Donaldson, Wang, and PhongSturm, we show that the statement holds for higher rank vector bundles over compact algebraic manifolds of arbitrary dimension that admit constant scalar curvature metric and have discrete automorphism group.

01/21/09
Craig Citro  UCLA, Developer
The ``Killer Apps'' in Sage: Cython, Interact, and 3d Graphics

01/21/09
Michael Abshoff  Dortmund, Sage Release Manager
The Sage Community

01/22/09
Amy Irwin  UCSD
Quaternion Algebras

01/22/09
Alex Eustis  UCSD
A Weighted Tiling Model for Continued Fractions
AbstractEver been curious about continued fractions? This talk will cover the basics, and demonstrate how they are closely related to weighted squareanddomino tilings. In particular we'll do a neat bijection that "compresses" a board with periodic weights into a smaller period1 board, and then show how this can be used to calculate periodic continued fractions. In addition, one can prove a number of Fibonacci/Lucas identities combinatorially using this model.

01/22/09
Moe Ebrahimi  UCSD
MHD Equation

01/22/09
Peter Stevenhagen  Universiteit Leiden
Prime divisors of linear recurrent sequences
AbstractFor many integer sequences $X=(x_n)_n$, it is
a natural question to describe the set $P_X$ of all
prime numbers $p$ that divide some nonzero term
of the sequence, and to quantify the `size' of $P_X$. \\\noindent We focus on the case of linear recurrent sequences,
where we have fairly complete results for recurrences
of order 2 based on the Chebotarev density theorem,
and mostly open questions for higher order recurrences. 
01/22/09
Evan Fuller  UCSD
Helping InService Teachers Advance Their Understanding of Proof
AbstractAs part of a summer professional development institute, we investigated how a focus on the explanatory power of different proofs helped inservice teachers enhance their understanding of mathematical proof. I will present example problems and several solutions in order to illustrate different types of proof and what we mean by explanatory power. In addition, I will discuss the different types of teaching practices that the instructor of the institute used in order to facilitate changes in participants' understanding of proof. This talk is intended for undergrads, grads, and professors.

01/22/09
Piotr Senty  University of Warsaw, Poland
Hydrophobic Effects in Vicinity of Concave Nanoscopic Objects
AbstractI will present results of molecular dynamics simulations of hemispherical hydrophobic pockets remaining in direct contact with water. The considered pockets of three different sizes represent simple models of nonpolar cavities often found in proteins' binding sites where they are important for hydrophobic interactions with ligands. A detailed analysis of solvent behaviour reveals significant density fluctuations inside the pockets resulting from cooperative movements of individual water molecules. \\
\noindent I will also consider a process of translocation of methane molecule from bulk solvent into the pockets and discuss the obtained potentials of mean force. Their analysis in the light of observed changes in water distribution around the interacting hydrophobic

01/22/09
David Whitehouse  Massachusetts Institute of Technology
On the automorphic transfer between locally isomorphic groups
AbstractRecent work of G. Prasad and Rapinchuk has produced families of groups which are locally isomorphic but not globally isomorphic. In the case of unitary groups associated to division algebras with an involution of the second kind we describe the corresponding Langlands functoriality between their automorphic representations.

01/22/09
J. Milne Anderson  University College, London University
The Logarithmic Derivative of a Polynomial
AbstractIf $Q_N(z)$ is a polynomial of degree $N$ and $P > 0$, then estimates for the size of the set where the logarithmic derivative $Q'(z)/Q(z)$ has modulus greater than P are given in terms of $P$ and $N$. These estimates are shown to be essentially the best possible. This is joint work with V. Ya. Eiderman.

01/23/09
Jun Li  UC Riverside
Multivariate Spacings Based on Data Depth and Construction of Nonparametric Multivariate Tolerance Regions
AbstractIn this talk, we introduce and study multivariate spacings. The spacings are
developed using the order statistics derived from data depth. Specifically,
the spacing between two consecutive order statistics is the region which
bridges the two order statistics, in the sense that the region contains all
the points whose depth values fall between the depth values of the two
consecutive order statistics. These multivariate spacings can be viewed as a
datadriven realization of the socalled ``statistically equivalent blocks".
These spacings assume a form of centeroutward layers of ``shells" (``rings"
in the twodimensional case), where the shapes of the shells follow closely
the underlying probabilistic geometry. The properties and applications of
these spacings are studied. In particular, the spacings are used to
construct tolerance regions. The construction of tolerance regions is
nonparametric and completely data driven, and the resulting tolerance region
reflects the true geometry of the underlying distribution. This is different
from most existing approaches which require that the shape of the tolerance
region be specified in advance. The proposed tolerance regions are shown to
meet the prescribed specifications, in terms of $\beta$$content$ and
$\beta$$expectation$. They are also asymptotically minimal under elliptical
distributions. Finally, we present a simulation and comparison study on the
proposed tolerance regions. \\\noindent This is joint work with Prof. Regina Y. Liu from Rutgers University.

01/27/09
Nitu Kitchloo  UCSD
Applications of Morse theory

01/27/09
Zhongming Wang  UCSD \\ Biochemistry and Mathematics
A LevelSet Variational ImplicitSolvent Approach to Hydrophobic Interactions
AbstractHydrophobic interactions drive relatively apolar molecules to stick together
in an aqueous solution. Such interactions are crucial to the structure,
dynamics, and function of biological systems. The implicit (or continuum) solvent approach is an efficient
way to model such interactions. In this talk, I will first describe a class of variational
implicitsolvent models for solvation. Central in these models isÂ a
freeenergy functional of all possibleÂ solutesolvent interfaces, coupling both
nonpolar and polar contributions.Â Minimization of this freeenergy functional
determines equilibrium solutesolvent interfaces which conceptually replace
solvent accessible surfaces (SAS) or solvent excluded surfaces (SES). I will then
describe a levelset method for capturing equilibrium solutesolvent interfaces.
In our levelset method, a possible solutesolvent interface is represented by the zero
level set (i.e., the zero level surface) of a function and
is evolved to reduce the free energy of the system, eventually intoÃƒï¿½Ã‚Â an equilibrium solutesolvent interface.
ThisÃƒï¿½Ã‚Â method is applied to the study of a large concave wall in water, together with a
small solute molecule. Our levelset calculations determine the solutesolvent interface locations and free energies very accurately
compared with molecular dynamics simulations that have been previously reported.
We also capture the bimodal behavior of the potential of mean force of the underlying hydrophobic interactions.
In addition, we find the curvature correction to the surface tension has a significant influence on the solutesolvent
interface profile in the concave region. All these demonstrate that our meanfield approach and numerical techniques
are capable of efficiently and accurately describing hydrophobic interactions with significant geometric influences.
This is joint work with LiTien Cheng, Piotr Setny, Joachim Dzubiella, Bo Li, and J. Andrew McCammon. 
01/27/09
Todd Kemp  Massachusetts Institute of Technology
Resolvents of $R$Diagonal Operators
Abstract\indent Random matrix theory, a very young subject, studies the behaviour of the eigenvalues of matrices with random entries (with specified correlations). When all entries are independent (the simplest interesting assumption), a universal law emerges: essentially regardless of the laws of the entries, the eigenvalues become uniformly distributed in the unit disc as the matrix size increases. This {\em circular law} was first proved, with strong assumptions, in the 1980s; the current state of the art, due to Tao and Vu, with very weak assumptions, is less than a year old. It is the {\em universality} of the law that is of key interest. \\
\indent What if the entries are {\em not independent}? Of course, much more complex behaviour is possible in general. In the 1990s, ``$R$diagonal'' matrix ensembles were introduced; they form a large class of nonnormal random matrices with (typically) nonindependent entries. In the last decade, they have found many uses in operator theory and free probability; most notably, they feature prominently in Haagerup's recent work towards proving the invariant subspace conjecture. \\
\indent In this lecture, I will discuss my recent joint work with Haagerup and Speicher, where we prove a universal law for the resolvent of any $R$diagonal operator. The circular ensemble is an important special case. The rate of blowup is, in fact universal among {\em all} $R$diagonal operators, with a constant depending only on their fourth moment. The proof intertwines both complex analysis and combinatorics.\\This talk will assume no knowledge of random matrix theory or free probability.

01/27/09
Sergey Kitaev  The Mathematics Institute, Reykjavik University
Generalized pattern avoidance, beta(1,0)trees, and 2stack sortable permutations
Abstract\indent The subject of pattern avoiding permutations has its roots in
computer science, namely in the problem of sorting a permutation
through a stack. A formula for the number of permutations of length
$n$ that can be sorted by passing it twice through a stack (where
the letters on the stack have to be in increasing order) was
conjectured by West, and later proved by Zeilberger. Goulden and
West found a bijection from such permutations to certain planar
maps, and later Cori, Jacquard and Schaeffer presented a bijection
from these planar maps to certain labeled plane trees, called
beta(1,0)trees.\indent We show that these labeled plane trees are in onetoone
correspondence with permutations that avoid the generalized patterns
3142 and 2413. We do this by establishing a bijection between
the avoiders and the trees. This bijection translates 7 statistics
on the trees into statistics on the avoiders.\noindent Moreover, extensive computations suggest that the
avoiders are structurally more closely connected to the
beta(1,0)treesand thus to the planar mapsthan twostack
sortable
permutations are.In connection with this we give a nontrivial involution on the
beta(1,0)trees, which specializes to an involution on unlabeled
rooted
plane trees, where it yields interesting results. 
01/29/09
Andy Linshaw  UCSD
Cyclic algebras

01/29/09
Vladimir Pesic  UCSD
Reflected Brownian Motion

01/29/09
Michael Volpato  UCSD
Integral embeddings of quaternions into octonions
AbstractWe study a SiegelWeil identity between a theta series and
an Eisenstein series of genus three. In particular, this yields a
Siegel modular form of genus three whose Fourier coefficients count
the number of arithmetic embeddings of definite quaternion orders into
the Coxeter order of integral octonions. 
01/29/09
Sergiu Klainerman  Princeton University
Why Black Holes are exciting mathematical objects
AbstractI will talk about some of the main open problems
in the theory of Black Holes. I will talk in particular
on recent results concerning uniqueness and stability. 
01/30/09
Liudmila Sabinina  University of Morelos, Mexico
Compact Moufang Loops with torsion

01/30/09
Sergiu Klainerman  Princeton University
On Hawking's uniqueness theorem, without analyticity
AbstractI will describe recent results of IonescuKlainerman
and AlexakisIonescuKlainerman which remove the crucial
assumption of analyticity in the
well known result of Hawking, Carter and Robinson
concerning the uniqueness of the Kerr solution among
stationary solutions.
Feb

02/02/09
Sue Sierra  University of Washington/Princeton University
Classifying birationally commutative projective surfaces
AbstractA {\em noncommutative projective surface} is a noetherian graded domain of GelfandKirillov dimension 3; their classification is one of the most important areas of research in noncommutative algebraic geometry. We complete an important special case by classifying all noncommutative projective surfaces that are {\em birationally commutative}: to wit, they are graded subrings of a skew polynomial ring over a field. We show that birationally commutative projective surfaces fall into four families, parameterized by geometric data, and we obtain precise information on the possible forms of this data. This extends results of Rogalski and Stafford on rings generated in degree 1, although our proof techniques are significantly different.

02/02/09
Jon Grice  UCSD
Discrete Quantum Control

02/03/09
Douglas Overholser  UCSD
Gradient flows and the Morse complex

02/03/09
Vyacheslav Kungurtsev  UCSD
InertiaControlling Factorization

02/03/09
Atsushi Ichino  Institute for Advanced Studies
On the KottwitzShelstad transfer factor for automorphic induction for GL(n)
AbstractFor a reductive group G and its endoscopic group H over a padic field, the functorial transfer from H to G should be characterized in terms of the character identity. For automorphic induction for GL(n), this identity was established by Henniart and Herb, up to a constant. We discuss a relation of this constant to the KottwitzShelstad transfer factor, in particular, to the epsilon factor normalization.

02/03/09
Raanan Schul  UCLA
BiLipschitz decomposition of Lipschitz functions into a metric space.
AbstractWe will outline the proof of a quantitative version of the following Sard
type theorem. Given a Lipschitz function $f$ from the $k$dimensional unit
cube into a general metric space, one can decomposed $f$ into a finite
number of BiLipschitz functions $f_{F_i}$ so that the $k$Hausdorff
content of $f([0, 1]^k \smallsetminus \cup F_i$) is small. The case where
the metric space is $\mathbb{R}^d$ is a theorem of P. Jones (1988). This
positively answers problem 11.13 in ``Fractured Fractals and Broken
Dreams" by G. David and S. Semmes, or equivalently, question 9 from
``Thirtythree yes or no questions about mappings, measures, and metrics"
by J. Heinonen and S. Semmes. 
02/05/09
Dan Rogalski  UCSD
Cyclic Algebras II

02/05/09
Victor Snaith  The University of Sheffield, UK
Computer calculations of the Borel regulator

02/05/09
Jozsef Balogh  University of Illinois, UrbanaChampaign
Recent Progress in Bootstrap Percolation
Abstract\indent Bootstrap percolation is the following deterministic process on a graph
$G$. Given a set $A$ of initially `infected' vertices, and a threshold $r
\in \mathbb{N}$, new vertices are subsequently infected if they have at
least $r$ previously infected neighbours. The study of this model
originated in statistical physics, and the process is closely related to
the Ising model. The set $A$ is usually chosen randomly, each vertex being
infected independently with probability $p \in (0,1)$, and the main aim is
to determine the critical probability $p_c(G,r)$ at which percolation
(infection of the entire graph) becomes likely to occur.\\I will give a survey of the area, focusing on the following recent result,
proved jointly with Bollobas and Morris:\\The bootstrap process has been extensively studied on the $d$dimensional
grid $[n]^d$, with $2 \le r \le d$, and it was proved by Cerf and Manzo
(building on work of Aizenman and Lebowitz, and Cerf and Cirillo) that
$$p_c\big( [n]^d,r \big) \; = \; \Theta\left( \frac{1}{\log_{r1} n}
\right)^{dr+1},$$ where $\log_{r1}$ is the $(r1)$times iterated
logarithm. However, the exact threshold function was only known in the case
$d = r = 2$, where it was shown by Holroyd to be $(1 +
o(1))\frac{\pi^2}{18\log n}$. In this talk we show how to determine the
exact threshold for all fixed $d$ and $r$, concentrating on the crucial
case $d = r = 3$. 
02/06/09
Mihoko Minami  The Institute of Statistical Mathematics, Japan
Statistical Challenges for Modeling Data with Many Zeros: A New Feature Extraction Method for Very NonNormal Data
AbstractData that we encounter in practice often have meny zerovalued
observations. Anaylizing such data without any consideration given
to how the zeros arose might lead to misleading results. In this talk,
we propose a new feature extraction method for very nonnormal data.
Our method extends principle component analysis (PCA) in the same
manner as the generalized linear model extends the ordinary linear
regression model. As an example, we analyze multivariate speciessize
data from a purseseine fishery in the eastern Pacific Ocean.
The data contain many zerovalued observations for each variable
(combinations of species and size). Thus, as an error distribution we
use the Tweedie distribution which has a probability mass at zero and
apply Tweediegeneralized PCA (GPCA) method to the data. 
02/09/09
Antonio Giambruno  University of Palermo, Italy
Polynomial identities and exponential growth

02/10/09
John Foley  UCSD
MorseBott theory

02/10/09
Ridgeway Scott  University of Chicago
The Mathematical Basis for Molecular van der Waals Forces

02/10/09
Sergey Kitaev  Reykjavik University
Permutations, sequences, and partially ordered sets
AbstractI will present some results from a recently completed project that ties together several objects: restricted in a certain way permutations, $(2+2)$free partially ordered sets, and a certain class of involutions (chord diagrams). Each of these structures can be encoded by a special sequence of numbers, called ascent sequences, thus providing bijections, preserving numerous statistics, between the objects.\\
\noindent In my talk, I will also discuss the generating function for these classes of objects, as well as a restriction on the ascent sequences that allows to settle a conjecture of Pudwell on permutations avoiding $3\bar{1}52\bar{4}$.\\
\noindent This is joint work with Mireille BousquetMelou (Bordeaux), Anders Claesson (Reykjavik University) and Mark Dukes (University of Iceland).

02/10/09
Dmitry Gourevitch  Weizmann Institute of Science
Gelfand pairs and invariant distributions

02/11/09
Oleg R. Musin  University of Texas, Brownsville
The kissing problem in three and four dimensions
AbstractThe kissing number $k(n)$ is the maximal number of equal nonoverlapping
spheres in $n$dimensional space that can touch another sphere of the same
size. This problem in dimension three was the subject of a famous
discussion between Isaac Newton and David Gregory in 1694. In three
dimensions the problem was finally solved only in 1953 by Sch\"utte and 
02/11/09
Dmitry Gourevitch  Weizmann Institute of Science
Multiplicity One Theorems  a uniform proof
AbstractLet F be a local field of characteristic 0. We consider distributions on GL(n+1,F) which are invariant under the adjoint action of GL(n,F). We prove that such
distributions are invariant under transposition. This implies that an irreducible representation of GL(n+1,F), when restricted to GL(n,F) "decomposes" with multiplicity one.Such property of a group and a subgroup is called strong Gelfand property. It is used in representation theory and automorphic forms. This property was introduced by Gelfand in the 50s for compact groups. However, for noncompact groups it is much more difficult to establish.
For our pair (GL(n+1,F),GL(n,F)) it was proven in 2007 in [AGRS] for nonArchimedean F, and in 2008 in [AG] and [SZ] for Archimedean F. In this lecture we will
present a new proof which is uniform for both cases. This proof is based on the above papers and an additional new tool. If time permits we will discuss similar
theorems that hold for orthogonal and unitary groups. 
02/12/09
Michele D'Adderio  UCSD
Crossed product algebras

02/12/09
Kiran Kedlaya  Massachusetts Institute of Technology
Formal classification of flat connections
AbstractThis talk will give an example of ideas from number theory
being deployed in the service of complex analytic geometry. We consider
the problem of the formal classification of flat meromorphic connections
on a complex manifold. We will first recall the answer in the
onedimensional case (the TurrittinLevelt theorem) and its relevance to
the asymptotic behavior of solutions of meromorphic differential
equations (the Stokes decomposition). We will then describe a
higherdimensional analogue, whose proof is much subtler: it uses
analytic geometry not just over the complex numbers, but also over
certain complete nonarchimedean fields (e.g., formal power series). The
methods we use are ultimately inspired by Dwork's study of the padic
variation of zeta functions of algebraic varieties. 
02/12/09
Neal Harris  UCSD
Arrow's Impossibility Theorem
AbstractIn 1951, Kenneth Arrow showed that under a reasonable definition of 'fair', there is no fair election system in a society of at least two individuals with at least three options. We'll make this statement into a precise theorem, prove it, and then discuss a generalization. While axioms and choice will both appear in this talk, the Axiom of Choice will not.

02/12/09
Yuhui Cheng  UCSD
Progress on the cellular Ca2+ diffusion studies using the realistic ttubule geometry
AbstractA tight coupling between cell structure, ionic fluxes and intracellular Ca2+ transients underlies the regulation of cardiac cell function. To investigate how a distribution of Ca2+ handling proteins may affect these coupled processes we developed a 3D model of Ca2+signaling, buffering and diffusion in rat ventricular myocytes. The model geometry was derived from the experiment. A diffusion modeling software using finite element tool kit (FEtK) libraries was implemented to solve the 4 coupled PDE systems. We concluded that the cardiac cell function is tightly regulated by the localization of Ca2+handling proteins and strongly relays on the presence of mobile and stationary Ca2+ buffers and cell geometry.

02/12/09
Abhishek Saha  California Institute of Technology
Lfunctions for GSp(4) X GL(2) and their critical values
AbstractIf M is an arithmetic or geometric object, one can often attach to it a complex analytic function L(M,s). This is called the Lfunction of M and provides a powerful tool to study its various properties. We will consider the case when M= (F,g) where F is a Siegel modular form of genus two and g a classical modular form. In this setup we prove the following result: for s lying in a certain set of so called critical points, the corresponding values L(M,s) are algebraic numbers up to certain period integrals and behave nicely under automorphisms. This is predicted by an old conjecture of Deligne on motivic Lfunctions. The main tool used in our proof is an integral representation of the Lfunction involving the pullback of an Eisenstein series defined on a unitary group.

02/12/09
Wei Biao Wu  University of Chicago
Some New Perspectives in the Theory of Time Series
AbstractI will present a unified framework for a largesample theory of
stationary and nonstationary processes. Topics in classical time
series analysis will be revisited and they include the estimation
of covariances, spectral densities and longrun variances. I will
also talk about high dimensional covariance matrices estimation
and inference of mean and quantiles of nonstationary processes. 
02/12/09
Alina Ioana Bucur  Massachusetts Institute of Technology
Multiple Dirichlet series
AbstractIn this talk we will explain how multiple Dirichlet series can be
employed to exploit analysis in several complex variables in order to
obtain arithmetic information. Then we will talk about their connections
to Weyl groups and KacMoody algebras. 
02/17/09
Ben Wilson  UCSD
Circlevalued Morse theory

02/17/09
Yiannis Sakellaridis  University of Toronto
A ``relative'' Langlands program and periods of automorphic forms.
AbstractMotivated by the relative trace formula of Jacquet and experience
on period integrals of automorphic forms, we take the first steps towards
formulating a ``relative'' Langlands program, i.e. a set of conjectures on
Hdistinguished representations of a reductive group G (both locally and
globally), where H is a spherical subgroup of G. We prove several results in
this direction. Locally, the spectrum of H/G is described with the help of
the dual group associated to any spherical variety by Gaitsgory and Nadler.
Globally, period integrals are conjectured to be Euler products of explicit
local functionals, which we compute at unramified places and show that they
are equal to quotients of Lvalues. If time permits, I will also discuss an
approach which shows that different integral techniques for representing
Lfunctions (e.g. Tate integrals, RankinSelberg integrals, period
integrals) are, in fact, the same. This is in part joint work with Akshay
Venkatesh. 
02/17/09
Louis Rowen  BarIlan University
Quivers of Representations and Applications to Polynomial Identities

02/17/09
Stefaan de Winter  Ghent University (Belgium)
Projective Planes and $C_4$free graphs that maximize the number of six cycles.
AbstractIt is a classical problem in graph theory to look for those graphs that maximize the number of copies of a subgraph H and are Ffree; the Turan problem being the most well known example of such problem. In this talk I will explain how the incidence graphs of projective planes of order $n$ are exactly those $n$ by $n$ bipartite graphs that are $C_4$free and maximize the number of eight cycles. An analogous characterization of projective planes as $C_4$free graphs that maximize the number of six cycles was previously known. I will also explain how a more general conjectural characterization of (the incidence graphs of) projective planes relates to some interesting geometric questions on projective planes. Finally I will mention some related open problems concerning socalled generalized polygons.

02/19/09
Joel Dodge  UCSD
Galois Cohomology

02/19/09
Valentino Tosatti  Harvard University
KahlerRicci flow and stability
AbstractI will discuss the relationship between convergence of the Ricci flow on a Fano manifold and algebraic stability of the manifold with the anticanonical polarization. I will show that if the curvature remains bounded along the flow then stability implies convergence of the flow and so in particular existence of a KahlerEinstein metric.

02/19/09
Chris Schroeder  UCSD, Department of Physics
Computational Particle Physics: Is the HIggs Boson a Technicolor Meson?
AbstractDetecting the Higgs boson is one of the highest priorities of the current
generation of particle physicists. While the Higgs may be a fundamental
particle, the interesting possibility exists that it is instead composed
of "quarks" of a new gauge theory at a higher energy scale, termed
Technicolor. In fact, the Higgs is expected to be discovered at the Large
Hadron Collider in the next two years, and if the particle's mass is on or
above a certain, not unreasonable scale, then a form of Technicolor may
become a prime candidate to explain its origin. I will describe this
puzzle and numerical methods which we are utilizing to explore it. 
02/19/09
PingShun Chan  UCSD
Character identities of the local packets of GSp(4).
AbstractW. T. Gan and S. Takeda have defined the local packets of GSp(4) using theta correspondence. We shall discuss how to use the trace formula technique to derive character identities satisfied by these packets.

02/19/09
Gabor Szekelyhidi  Columbia University
Greatest lower bounds on the Ricci curvature of Fano manifolds
AbstractOn Fano manifolds we study the supremum of the possible t such that there exists a metric in the first Chern class with Ricci curvature bounded below by t. For the projective plane blown up in one point we show that this supremum is 6/7.

02/19/09
Michael P. Friedlander  University of British Columbia
Algorithms for largescale sparse reconstruction
AbstractMany signalprocessing applications seek to approximate a signal as a superposition of only a few elementary atoms drawn from a large collection. This is known as sparse reconstruction. The theory of compressed sensing allows us to pose sparse reconstruction problems as structured convex optimization problems. I will discuss the role of duality in revealing some unexpected and useful properties of these problems, and will show how they lead to practical, largescale algorithms. I will also describe some applications of the resulting algorithms.

02/24/09
Ben Hummon  UCSD
Graph flows and Fukaya's Morse category

02/24/09
Michael Ferry  UCSD
A Subspace Minimization Method for Constrained Optimization

02/24/09
Fan Chung Graham  UCSD
Open problems in graph theory

02/26/09
Daniel Vallieres  UCSD
Brauer groups of local fields

02/26/09
Firas RassoulAgha  University of Utah
On the almostsure invariance principle for random walk in random environment
Abstract\indent Consider a crystal formed of two types of atoms placed at the nodes of the integer lattice. The type of each atom is chosen at random, but the crystal is statistically shiftinvariant. Consider next an electron hopping from atom to atom. This electron performs a random walk on the integer lattice with randomly chosen transition probabilities (since the configuration seen by the electron is different at each lattice site). This process is highly nonMarkovian, due to the interaction between the walk and the environment.
We will present a martingale approach to proving the invariance principle (i.e. Gaussian fluctuations from the mean) for (irreversible) Markov chains and show how this can be transferred to a result for the above process (called random walk in random environment).
This is joint work with Timo Seppalainen.

02/26/09
Chris Deotte  UCSD
Parallel Processing, Math, and MPI
AbstractWe will explore the process of solving a math problem using parallel
processing and MPI. As an example, we will solve a discrete Poisson
equation using Jacobi's method. Basic issues in developing, optimizing,
and deploying parallel algorithms on a cluster of CPU's will be discussed. 
02/26/09
Yangjin Kim  Ohio State University
Glioma invasion and microenvironment : a PDE/multiscale model
AbstractGlioma (brain tumor) invasion depends on its microenvironment. We will present two models in this talk. We first analyze the migration patterns of glioma cells from the main tumor, and show that the various patterns observed in experiments can be obtained by a model's simulations, by choosing appropriate values for some of the parameters (chemotaxis, haptotaxis, and adhesion) of the PDE model. For the second part of talk, we introduce a multiscale model in order to get more detailed informations on cell migration. The results of such an approach are compared to the experimental data as well.
*This is joint work with Avner Friedman (MBI), Sean Lawler, Michal O. Nowicki, E. Antonio Chiocca (Oncological Neurosurgery), Jed Johnson, John Lannutti (Lannutti lab) at the Ohio State University, and Hans Othmer (University of Minnesota).

02/26/09
Burkhard Wilking  Univ. Muenster
Ricci flow in high dimensions
AbstractWe consider a very simple curvature condition:
Given constant $c$ and a dimension $n$ we say that a
manifold $(M,g)$ satisfies the condition (c,n) if the scalar
curvature is bounded below by c times the norm of the Weyl
curvature. We show that in each large even dimensions there is precisely one
constant $c^2=2(n1)(n2)$ such that this condition is invariant under
the Ricci flow.The condition behaves very similar to scalar curvature under conformal
transformations
and we indicate how this can be utilized to get a large source of examples.
Finally we speculate what kind singularities should develop under the
Ricci flow. 
02/27/09
René Schoof  Universita di Roma ``Tor Vergata''
The analogy between number fields and algebraic curves: Arakelov meets Tate
Mar

03/02/09
Olga Kharlampovich  McGill University \\ Montreal, Canada
Around Tarski's problems and beyond
AbstractI will discuss our solution (joint with A. Myasnikov) of Tarski's
problems about elementary theory of free groups,
new techniques and directions that resulted from this solution. 
03/03/09
Amy Irwin  UCSD
Combinatorial Morse Theory

03/03/09
Elizabeth Wong  UCSD
An SQP Method for Nonlinear Optimization
AbstractWe present a sequential quadratic programming (SQP)
algorithm for nonlinear optimization. We give a
brief overview of SQP methods in general and then
describe an activeset method based on inertia control
for solving the convex quadratic subproblems. We also
discuss the motivation behind this algorithm as well as
its applications. 
03/03/09
Bruno Pelletier  Univ. Montpellier II
Clustering with level sets
AbstractThe objective of clustering, or unsupervised classification, is to partition a set of observations into different groups, or clusters, based on their similarities. Following Hartigan, a cluster is defined as a connected component of an upper level set of the underlying density. In this talk, we introduce a spectral clustering algorithm on estimated level sets, and we establish its strong consistency. We also discuss the estimation of the number of connected components of density level sets.

03/03/09
Sergey Kitaev  Reykjavík University
Crucial words for abelian powers
AbstractIn 1961, Erdös asked whether or not there exist words of
arbitrary length over a fixed finite alphabet that avoid patterns of the
form $XX'$ where $X'$ is a permutation of $X$ (called "abelian squares"). This
problem has since been solved in the affirmative in a series of papers
from 1968 to 1992. A natural generalization of the problem is to study
"abelian kth powers", i.e., words of the form $X_1X_2...X_k $where $X_i$ is
a permutation of $X_1$ for $2 \le i \le k$.
In this talk, I will discuss "crucial words" for abelian kth powers,
i.e., finite words that avoid abelian kth powers, but which cannot be
extended to the right by any letter of their own alphabets without
creating an abelian kth power. More specifically, I will consider the
problem of determining the minimal length of a crucial word avoiding
abelian kth powers. This problem has already been solved for abelian
squares by Evdokimov and Kitaev (2004). I will present a solution for
abelian cubes (the case k = 3) and state a conjectured solution for the
case of $k \ge 4.$This is joint work with Amy Glen and Bjarni V. Halldórsson (Reykjavík
University). 
03/04/09
Burkhard Wilking  Muester University
High dimensional Ricci flow

03/05/09
Zhou Zhou  University of Chicago
Nonstationary time series analysisa nonlinear systems approach

03/05/09
Vyacheslav Kungurtsev  UCSD
The Conformal Thin Sandwich Method in General Relativity
AbstractEinstein's constraint equations govern the geometric properties of spacetime in relation to matter and energy. Motivated by the preservation of the fulfillment of these constraints in a Hamiltonian formulation, the conformal thin sandwich method is a successful approach to determining the solution in a number of parameter classes.

03/05/09
Harold Stark  UCSD
TBA Part II

03/05/09
Claudio Procesi  University of Rome
The Spirit of Algebra
AbstractWe will start with a quick excursion into some of the highlights of the
history of Algebra. This leads to some present trends which connect
Algebra to several other areas of Mathematics from Algebraic Geometry and
Topology to pure and applied Analysis. These topics will be illustrated
through some concrete examples, such as quantum groups, braid groups,
wonderful models, toric arrangements, splines, equivariant $K$theory and
the index theorem. 
03/10/09
Justin Roberts  UCSD
Floer homology and Morse theory

03/10/09
Joey Reed  UCSD
Multigrid Methods in Optimization
AbstractThere are many methods one may use to solve partial
differential equations numerically. For large scale
problems, direct methods are not computationally
feasible and therefore iterative methods tend to be the
best option. Multigrid methods are a particularly
attractive strategy for certain classes of
problems. Roughly speaking, in a multigrid approach, a
problem is solved on a hierarchy of grids. The purpose
of this talk is to discuss the benefits of a multigrid
strategy and various ways it may be introduced in
optimization. Of particular interest is the so called
nonlinear multigrid scheme. 
03/11/09
Ezra Getlzer  Northwestern University
ngroups
AbstractIn this talk, we give a brief introduction to a natural
generalization of groups, called ngroups.\\Just as discrete groups represent the homotopy types of acyclic spaces,
ngroups realize homotopy types of connected topological spaces $X$ such that
$\pi_i(X)=0$ for $i>n$. In this talk, we adopt the formalism of simplicial sets,
and define ngroups as simplicial sets satisfying certain a filling
condition (introduced by Duskin).\\In the first part of the talk, we explain what a 2group look like: this
material is contained in any textbook on simplicial sets. We indicate how
2groups arise in topological quantum field theory. 
03/12/09
Adrian Wadsworth  UCSD
Brauer groups of local, global, complete valued fields and rational function fields

03/12/09
Nicolas Lanchier  Arizona State University
Coexistence in spatially explicit metapopulations
AbstractThe multitype contact process is a stochastic model including space in the form of local interactions and describing the evolution of two species competing on a connected graph. While it is conjectured for the multitype contact process on the two dimensional regular lattice that, regardless of their birth and death rates, species cannot coexist at equilibrium, we prove that two species with opposite strategies (specialist versus generalist) coexist on a connected graph including two levels of interactions.

03/12/09
Angela Hicks  UCSD
Combinatorics of the Diagonal Harmonics
AbstractThe space of diagonal harmonics has emerged as one of the key ingredients in a program initiated by Garsia and Haiman to give a representationtheoretical proof of some conjectures in the theory of Macdonald polynomials.
The study of this particular space has provided a remarkable display of connections between several areas, including representation theory, symmetric function theory, and combinatorics. Over two decades since the introduction of the diagonal harmonics, the bivariate Hilbert series of the diagonal harmonics has been the object of a variety of algebraic and combinatorial conjectures. In the following lecture, we will define the diagonal harmonics and explore some of the combinatorial objects related to this space. We assume only a basic understanding of undergraduate algebra and a passing appreciation for either free food or beautiful mathematical pictures.

03/12/09
Madhusudhanan Balasubramanian  UCSD \\ Department of Ophthalmology
Computational Techniques for Estimating Progressive Deformation in the Optic Nerve Head Region of the Retina in Glaucoma
AbstractGlaucoma is the second leading cause of blindness worldwide. Often the optic nerve head (ONH) glaucomatous damage and ONH changes occur prior to loss of visual function and are observable in vivo. Thus, digital image analysis is a promising choice for detecting the onset and/or progression of glaucoma. In this work, we present a new framework for detecting glaucomatous changes in the ONH using the method of proper orthogonal decomposition (POD)1. A baseline topograph subspace is constructed using POD for each eye to describe the ONH structure of the eye at a reference/baseline condition. The bases that form the baseline subspace capture the topograph measurement variability and any inherent structure variability of the ONH at baseline. Any glaucomatous changes in the ONH of an eye present during a followup exam are estimated by comparing the ONH topograph acquired from the followup exam with its baseline topograph subspace representation. Image correspondence measures of correlation, Euclidean distance, and image Euclidean distance (IMED) are used to quantify the ONH changes. An ONH topograph library built from the Louisiana State University experimental glaucoma study is used to demonstrate the performance.

03/12/09
Ron Evans  UCSD
Hypergeometric functions over finite fields and Hecke eigenforms

03/16/09
Said Sidki  University of Brasilia, Brazil
Functionally Recursive Algebras

03/17/09
Xiaojun Huang  Rutgers University
A codimension two CR singular real submanifold in a complex space with a symmetric model
AbstractThis a joint work with Wanke Yin.
Let $M\subset \mathbb{C}^{n+1}$ ($n\ge 2$) be a real
analytic submanifold defined by an equation of the form:
$w=z^2+O(z^3)$, where we use $(z,w)\in {CC}^{n}\times CC$
for the coordinates of ${C}^{n+1}$. We first derive a pseudonormal form
for $M$ near $0$. We then use it to prove that $(M,0)$ is holomorphically
equivalent to the quadric $(M_\infty: w=z^2,\ 0)$ if and only if it can
be formally transformed to $(M_\infty,0)$, using the rapid convergence
method. We also use it to give a necessary and sufficient condition
when $(M,0)$ can be formally flattened. Our main theorem generalizes a
classical result of Moser for the case of $n=1$. 
03/17/09
Vladimir Kirichenko  Kiev State Univ., Ukraine
Quivers of associative rings
AbstractAll rings are associative with $1\not = 0$. A ring $A$ is decomposable if $A=A_{1}\times A_{2}$, otherwise $A$ is indecomposable.
We consider three types quivers of rings: Gabriel quiver, prime quiver and Pierce quiver.
Gabriel quiver and Pierce quiver are defined for semiperfect rings.
Let $A$ be an associative ring with the prime radical $Pr(A)$.
The factorring $\bar{A} = A/Pr(A)$
is called the diagonal of $A$. We say that a ring $A$ is a $FD$ring if $\bar{A}$ is a finite direct product
of indecomposable rings. We define the prime quiver of $FD$ring with $T$nilpotent prime radical.We discuss the properties of rings and its quivers, for example, a
right Noetherian semiperfect ring is semisimple Artinian if and only if
its Gabriel quiver is a disconnected union of vertices (without arrows). 
03/17/09
Sergey Kitaev  Reykjavik University
Graphs represented by words
AbstractGiven a word over some alphabet, we can form a graph with the letters of
the alphabet as vertices, and with two vertices adjacent if those
letters occur alternatingly in the word. A motivation for studying the
class of graphs represented by words (in the described manner) comes
from algebra, but another application is in robot scheduling.\\\noindent When considering a class of graphs, several immediate questions pop up:\\
\noindent  Which graphs belong (and which ones do not) to the class,\\
 How large do the words need to be to represent all such graphs, and\\
 Can we come up with alternative representations that in particular
make it easier to answer structural and algorithmic questions about
these graphs?\\I will discuss recent answers to these questions. This is joint work
with Magnus M. Halldorsson (Reykjavik University) and Artem Pyatkin
(Sobolev Institute of Mathematics). 
03/19/09
Bill Helton  UCSD
Welcome address: what is SCOD ?

03/19/09
Tom Bewley  UCSD
Incorporating Regular Lattices and Accounting for Approximate Function Evaluations in DerivativeFree Optimization
AbstractSystems characterized by expensive, nonconvex, noisy functions in moderate dimensions (n=2 to 24) necessitate the development of maximally efficient derivativefree optimization algorithms. Starting with the wellknown Surrogate Management Framework (SMF), our lab has developed a new, highly efficient derivativefree optimization algorithm, which we dub LAtticeBased Derivativefree Optimization via Global Surrogates (LABDOGS). This algorithm combines a highly efficient, globally convergent surrogatebased Search algorithm with an efficient Poll which incorporates a minimum number of new function evaluations chosen from nearestneighbor points. All function evaluations are coordinated with highly uniform noncartesian lattices derived from ndimensional sphere packing theory. Representative numerical tests confirm significant improvements in convergence of latticebased strategies as compared with otherwise identical codes coordinated using Cartesian grids.
The second topic of our talk focuses on incorporating approximate function evaluations into a surrogatebased optimization scheme. Assuming the accuracy of each function evaluation in a statistical setting diminishes towards zero in proportion with the reciprocal of the square root of the sample time, we have developed an algorithm for sampling the function only as accurately as warranted. The algorithm we have developed, dubbed $\alpha$DOGS, maintains the globally convergent behavior of the LABDOGS Search while focusing the bulk of the computation time on regions of parameter space where the existing approximate function evaluations indicate that the true function minimum might lie.

03/19/09
Shaowei Lin  UCB
Polynomial Relations among Principal Minors of a Matrix

03/19/09
Martin Harrison  UCSB
Minimal Sums of Squares in a free *algebra
AbstractIn this talk, I discuss the reduction of the number of squares needed to express a sum of squares in the free *algebra R. I will give examples of sums which are irreducible in this sense, and prove bounds on the minimal number of terms needed to express an arbitrary sum of squares of a given degree in a given number of variables

03/19/09
Gert Lanckriet  UCSD
TBA

03/19/09
Emre Mengi  UCSD
Lipschitzbased optimization of singular values
AbstractSingular value optimization problems arise in various applications in control theory. For instance the $H_{\infty}$ norm of the transfer function of a linear dynamical system, and the distance problems such as complex (or real) stability and controllability radii have singular value optimization characterizations. These problems are nonconvex and nonsmooth. The existing commonly employed algorithms for these problems are derivativefree, but do not exploit the Lipschitz nature of singular values in a systematic manner. Here we solve these problems largely depending on a Lipschitz optimization algorithm due to Piyavskii and Shubert, that never got attention in the context of optimization of eigenvalues or singular values. The PiyavskiiShubert based algorithm outperforms the commonly employed algorithms for medium to large scale problems when a few digit accuracy is sought.

03/19/09
Panagiota Daskalopoulos  Columbia University
Ancient solutions to the curve shortening flow and Ricci flow on surfaces

03/19/09
Paul Tseng  University of Washington
On SDP and ESDP Relaxation for Sensor Network Localization
AbstractRecently Wang, Zheng, Boyd, and Ye proposed a further convex relaxation of the SDP relaxation for the sensor network localization problem, which they called edgebased SDP (ESDP). The ESDP is easier to solve than the SDP and, in simulation, yields solution about as accurate as the SDP relaxation. We show that, when the distance measurements are exact, we can determine which sensors are correctly positioned in the ESDP solution by checking if their individual traces are zero. On the other hand, we show that, when the distance measurements are inexact, this check is unreliable for both ESDP and SDP solutions. We then propose a robust version of ESDP relaxation for which small individual trace is a reliable check of sensor position accuracy. Moreover, the position error for such a sensor is in the order of the square root of its trace. Lastly, we propose a coordinate gradient descent method, using logbarrier penalty, to solve ESDP. This method is more efficient than interiorpoint method for solving SDP or ESDP and is implementable in a distributed manner. (This is joint work with Ting Kei Pong.)

03/23/09
James Wilson  Ohio State University
Decomposing $p$groups via Jordan algebras
AbstractThere are at least $p^{2n^3/27+O(n^2)}$ groups of order $p^n$,
and in 2006 those of order $p^7$ were classified in over 600 pages of work.
Yet, with such a multitude of groups, a structure theory seems impossible.
One approach is to decompose the $p$groups via central
and related products to reduce the study to indecomposable groups. Using rings
and Jordan algebras, a theorem is proved on the uniqueness of these decompositions,
asymptotic estimates are given which show there are roughly equal numbers of
decomposable and indecomposable groups, and the indecomposable groups are
categorized into classical families.
Apr

04/02/09
Joseph Cessna  UCSD \\ Department of Mechanical and Aerospace Engineering
Structured computational interconnects on a sphere for the efficient parallel solution of the 2D shallowwater equations
AbstractThe efficient computation of complex flows on the sphere, governed by the 2D shallowwater equations, is of acute importance in the modeling and forecasting of weather phenomenon on the earth. Some of the most powerful supercomputer clusters every built have been fully dedicated to this problem. In the years to come, increased performance in such clusters will be derived in large part from massive parallelization, to tens of thousands and even hundreds of thousands of computational nodes in the cluster. To facilitate such scalability, switchless interconnect systems coordinating the communication within the cluster are absolutely essential, as such systems eliminate an otherwise significant bottleneck (that is, the switch) impeding the communication between the nodes.
The present work introduces a new switchless interconnect topology for supercomputer clusters which are dedicated specifically for computing such flows on the sphere. This topology is based on a class of Fullerenes (i.e., Buckyballs) with octahedral symmetry. In this topology, each node has direct send/receive capabilities with three neighboring nodes, and the cluster is itself physically connected in a spherical configuration. This natural correspondence between the interconnect network and the discretized physical model itself tends to keep most communication local (that is, between neighbors) during the flow simulation, thereby minimizing the density of packets being passed across the cluster and increasing dramatically the overall computational speed. One of the most communicationintensive steps of the flow simulation is related to solving the Poisson equation on the sphere; it is shown that the present topology is particularly well suited to this problem, leveraging multigrid acceleration with Red/Black GaussSeidel smoothing.

04/02/09
Eric Tressler  UCSD
Ramsey Theory: $2^{903}$ Steps to Fame

04/02/09
Leonard Gross  Cornell University
Spaces of geometric flows in quantum field theory
AbstractNo matter what discoveries are made at the Large Hadron Collider in Switzerland when it begins operating next year, its a sure thing that gauge fields (i.e., connections on vector bundles) will continue to play the central role in elementary particle theory that they have for the past 40 years.
The quantization of a pure gauge field amounts, informally, to the construction of a suitable measure on the configuration space of the gauge field, (i.e., the moduli space: connection forms modulo gauge transformations.) This is an infinite dimensional manifold which must be chosen large enough, in some distribution sense, to support this measure. In this talk I am going to show how one can hope to realize such nonlinear distribution spaces as spaces of geometric flows. Specifically, I will describe the state of the art for the YangMills heat equation on a three manifold with boundary.

04/07/09
Justin Roberts  UCSD
Introductory Meeting
AbstractThis term's plan is to read Jacob Lurie's new preprint:``On the classification of Topological Field Theories'', which is available on his MIT homepage. As usual, seminar participants will give the talks, and we'll try to parcel them out at the first meeting on April 7th. But everyone is welcome  we won't force you to speak if you don't want to! \\
\noindent In 1989 Atiyah (inspired by Segal and Witten) defined a TFT to be a monoidal functor from the category of (n+1)dimensional cobordisms to the category of vector spaces. That is, it assigns a vector space to each closed nmanifold, and linear maps between these to each (n+1)dimensional cobordism (that is, an (n+1)dimensional manifold whose boundary is divided into "ingoing" and "outgoing" parts), satisfying natural composition laws. The idea comes from quantum field theory, in which each slab of spacetime between "past" and "future" spacelike hypersurfaces should define a unitary map between their corresponding Hilbert spaces of states. The difference is that in QFT, the metrics on such spacetime cobordisms matter, whereas in TFT the linear maps depend only on the underlying topology of the cobordisms. The general formalism of QFT suggests that one should be able to extend this algebraic structure into lower dimensions, assigning a category to each (n1)dimensional manifold, a 2category to each (n2)dimensional manifold, and so on, ultimately assigning some kind of ncategory to the point: this ncategory ought to determine the whole TFT structure. Many attempts to formulate this sort of thing were made in the early 90s, but because of the lack of a solid definition of ``ncategory'', made little progress. One can also extend into higher dimensions: kparameter families of manifolds can be added into the picture, leading to theories in which the topology of diffeomorphism groups of manifolds enters naturally. A theory of this sort in 2 dimensions was worked out by Kevin Costello a few years ago under the name ``Topological Conformal Field Theory''. Lurie's new paper provides a complete formulation of TFTs incorporating all of the above features. He provides a solid definition of ncategories in the spirit of algebraic topology, and proves many foundational results about them. Then he shows how TFTs can be characterised using this language. In particular, he proves the remarkable ``BaezDolan cobordism hypothesis'', which states that the ncategory of ndimensional cobordisms is the free ncateg

04/07/09
Olvi Mangasarian  UCSD
PrivacyPreserving Support Vector Machine Classification Via Random Kernels
AbstractPrivacypreserving support vector machine (SVM) classifiers are proposed for vertically
and horizontally partitioned data. Vertically partitioned data represent instances where
distinct entities hold different groups of input space features for the same individuals, but
are not willing to share their data or make it public. Horizontally partitioned data
represent instances where all entities hold the same features for different groups of
individuals and also are not willing to share their data or make it public. By using a
random kernel formulation we are able to construct a secure privacypreserving kernel
classifier for both instances using all the data but without any entity revealing its
privately held data. Classification accuracy is better than an SVM classifier without
sharing data, and comparable to an SVM classifier where all the data is made public. 
04/07/09
Ameera Chowdhury  UCSD
Shadows and Intersections in Vector Spaces
AbstractWe introduce the area of extremal set theory via three
classical
results: the ErdosKo Rado theorem, Frankl's $r$wise intersection
theorem, and the KruskalKatona shadow theorem. We then consider vector
space analogs of these problems. We prove a vector space analog of a
version of the KruskalKatona theorem due to Lov\'{a}sz. We apply this
result to extend Frank's theorem on $r$wise intersecting families to
vector spaces. In particular, we obtain a short new proof of the
ErdosKoRado theorem for vector spaces. 
04/08/09
Owen Dearricott  UC Riverside
Positive curvature on 3Sasakian 7manifolds
AbstractWe discuss metrics of positive curvature on 3Sasakian 7manifolds including one on a new diffeomorphism type.

04/09/09
Allan Sly  University of California, Berkeley
Mixing in time and space
AbstractFor Markov random fields temporal mixing, the time it takes for the Glauber dynamics to approach its stationary distribution, is closely related to phase transitions in the spatial mixing properties of the measure such as uniqueness and the reconstruction problem. Such questions connect ideas from probability, statistical physics and theoretical computer science. I will survey some recent progress in understanding the mixing time of the Glauber dynamics as well as related results on spatial mixing.

04/09/09
Ari Stern  UCSD
Geometric aspects of ODEs and PDEs
AbstractIn this talk, I plan to discuss how differential geometry can provide useful insights into the study of ordinary and partial differential equations. In particular, I will focus on the role of symplectic geometry in classical Lagrangian and Hamiltonian mechanics, as well as its generalization to the multisymplectic geometry of classical field theory. Finally, I will talk about how this perspective has paved the way for the development of ``geometric'' numerical integrators, which exactly preserve important structures, symmetries, and invariants.

04/09/09
Eric Cances  Ecole des Ponts ParisTech, France
Some mathematical aspects of Density Functional Theory
AbstractElectronic structure calculations are commonly used to understand and predict the electronic, magnetic and optic properties of molecular systems and materials. They are also at the basis of ab initio molecular dynamics, the most reliable technique to investigate the atomic scale behavior of materials undergoing chemical reactions (oxidation, crack propagation, ...). In the first part of my talk, I will briefly review the foundations of the density functional theory for electronic structure calculations. In the second part, I will present some recent achievements in the field, as well as open problems. I will focus in particular on the mathematical modelling of defects in crystalline materials.

04/14/09
Ben Hummon  UCSD
$(\infty, n)$categories

04/14/09
Zhongming Wang  UCSD
A Bloch Band Based Level Set Method for Computing the Semiclassical limit of Schrodinger Equations
AbstractA novel Bloch band based level set method is proposed for computing
the semiclassical limit of Schrodinger equations in periodic media.
For the underlying equation subject to a highly oscillatory initial
data, a hybrid of the WKB approximation and homogenization leads to
the Bloch eigenvalue problem and an associated HamiltonJacobi system
for the phase in each Bloch band, with the Bloch eigenvalue be part
of the Hamiltonian. We formulate a level set description to capture
multivalued solutions to the band WKB system, and then evaluate
total homogenized density over a sample set of bands. A superposition
of band densities is established over all bands and solution branches
when away from caustic points. The numerical approach splits the
solution process into several parts: i) initialize the level set
function from the band decomposition of the initial data; ii) solve
the Bloch eigenvalue problem to compute Bloch waves; iii) evolve the
band level set equation to compute multivalued velocity and density
on each Bloch band; iv) evaluate the total position density over a
sample set of bands using Bloch waves and band densities obtained in
step ii) and iii), respectively. Numerical examples with different
number of bands are provided to demonstrate the good quality of the
method. 
04/14/09
Dan Knopf  University of Texas, Austin
Minimallyinvasive surgery for Ricci flow singularities
AbstractIf a solution (M,g(t)) of Ricci flow develops a local singularity at a finite time T, there is a proper subset S of M on which the curvature becomes infinite as time approaches T. Existing approaches to Ricciflowwithsurgery, due to Hamilton and Perelman, require one to modify the solution in a small neighborhood of S by gluing in a highly curved but nonetheless nonsingular solution. This must be done with careful regard to various surgery parameters in order to preserve critical a priori estimates. In case the local singularity is a rotationallysymmetric neckpinch (in any dimension $n>2$), we can now restart Ricci flow directly from the singular limit g(T), without performing an intervening surgery or making ad hoc choices. We show that any complete smooth forward evolution from g(T) is necessarily compact and has a unique asymptotic profile as it emerges from the singularity, which we describe. (This is joint work with Sigurd Angenent and Cristina Caputo.)

04/14/09
Leonard M. Sander  University of Michigan, Ann Arbor \\ Physics Department
A generalized CahnHilliard equation for biological applications
AbstractWe study fronts of cells such as those invading a wound or in a growing tumor. First we look at a discrete stochastic model in which cells can move, proliferate, and experience cellcell adhesion. We compare this with a coarsegrained, continuum description of this phenomenon by means of a generalized CahnHilliard equation (GCH) with a proliferation term.
There are two interesting regimes. For subcritical adhesion, there are propagating "pulled" fronts, similarly to those of FisherKolmogorov equation. The problem of front velocity selection is examined, and our theoretical predictions are in a good agreement with a numerical solution of the GCH equation. For supercritical adhesion, there is a nontrivial transient behavior. The results of continuum and discrete models are in a good agreement with each other for the different regimes we analyzed.

04/16/09
Natalia Komarova  University of California, Irvine
Stochastic modeling of cancer
AbstractEven though much progress has been made in mainstream experimental cancer research at the molecular level, traditional methodologies alone are sometimes insufficient to resolve important conceptual issues in cancer biology. In this talk, I will describe mathematical tools which help obtain new insights into the processes of cancer initiation, progression and treatment. The main idea is to study cancer as an evolutionary dynamical system on a selectionmutation network. I will discuss the following topics: Stem cells and tissue architecture; Stem cells and aging, and Drug resistance in CML.

04/16/09
Ravi Shroff  UCSD
An Introduction to Equivalence Problems for Real Hypersurfaces in Complex Space
AbstractA basic question in geometry and topology is to discover necessary (and perhaps sufficient) conditions for two manifolds to be locally or globally equivalent for some notion of equivalence. An example of a global topological invariant is the fundamental group of a topological space, because having isomorphic fundamental groups is a necessary condition for two spaces to be equivalent up to homotopy. We restrict ourselves to real hypersurfaces in $C^2$. I'll sketch Poincare's proof of the global inequivalence of the unit ball and polydisc, then outline a method due to Cartan, Chern, and Moser, about how to find a system of invariants for the local equivalence problem. Knowing a bit of differential geometry and complex analysis would be helpful, but isn't essential.

04/21/09
John Foley  UCSD
More on $(\infty, n)$categories

04/21/09
Harald Pfeiffer  Dept of Physics, Caltech
Binary black hole simulations and implicit timestepping
AbstractNumerical simulations of black hole binaries have made tremendous progress over the last years. The usefulness of such simulations is limited by their tremendous computational cost, which ultimately results from a separation of timescales: Emission of gravitational radiation drives the evolution of the binary toward smaller separation and eventual merger. The timescale for inspiral is far longer than the dynamical timescale of each black hole. Therefore, the currently deployed explicit timesteppers are severely limited by Courant instabilities. Implicit timestepping algorithms provide an obvious route around the Courant limit, thus offering a tremendous potential to speed up the simulations. However, the complexity of Einstein's equations make this a highly nontrivial endevour. This talk will first present a general overview of the status of Black Hole simulations, followed by a status report on the ongoing work aimed at implementing modern implict/explicit (IMEX) evolution schemes for Einstein's equations.

04/23/09
Grzegorz Banaszak  Univ. of Poznan, Poland
On Arithmetic in MordellWeil groups
AbstractLet $A/F$ be an abelian variety
over a number field $F$ and let $P \in A(F)$
and $\Lambda \subset A(F)$ be a subgroup of the MordellWeil group.
For a prime $v$ of good reduction let
$r_v : A(F) \rightarrow A_v (k_v)$ be the reduction map.
During my talk I will show that the condition $r_v (P) \in
r_v (\Lambda)$ for almost all primes $v$ implies that
$P \in \Lambda + A(F)_{tor}$ for a wide class of abelian varieties. 
04/23/09
Richard Libby  Barclays Global Investors
Mathematical Finance: How Logical Paradox Helped Decipher the Credit Crisis
AbstractRefreshments will be served at 3:30 P.M.\\
\noindent Richard Libby is responsible for counterparty risk oversight and control, related risk measurement and policy, operational and credit risk, economic and regulatory capital analysis, and model validation. \\
\noindent Prior to joining Barclays Global Investors in 1999, Richard was Vice President for Capital Markets Analytics at Bank of America with responsibility for credit derivatives and market risk systems and analytics. \\
\noindent Richard has a BA and MA in mathematics from the University of California, San Diego, and a PhD in mathematics from the University of California, Santa Cruz.

04/24/09
Chris Tiee  UCSD
Lorentz Invariance of Maxwell's Equations
AbstractWe convert the standard vector calculus description of Maxwell's Equations into the language of differential forms on Minkowski spacetime, which results in a very elegant reformulation (just two equations instead of four). We then show that this is actually invariant under Lorentz transformations, and describe what bothered Einstein so much that he had to formulate Special Relativity to fix things up.

04/24/09
Julie Rowlett  UC Santa Barbara
The Fundamental Gap Conjecture for Triangles
AbstractThe Fundamental Gap Conjecture due to S. T. Yau and M. van de Berg states that for a convex domain in $R^n$ with diameter $d$, the first two positive eigenvalues of the Dirichlet Laplacian satisfy \[\lambda_2  \lambda_1 \geq \frac{3 \pi^2}{d^2}.\] $\lambda_2  \lambda_1$ is known as the fundamental gap and has been studied by many authors. It is of natural interest to spectral geometers, and moreover, estimates for the fundamental gap have applications in analysis, statistical mechanics, quantum field theory, and numerical methods.
I will discuss joint work with Zhiqin Lu on the fundamental gap when the domain is a Euclidean triangle. Our first result is a compactness theorem for the gap function, which shows that the gap function is unbounded as a triangle collapses to a segment. I will outline our current work which indicates that the equilateral triangle is a strict local minimum for the gap function on triangular domains. Finally, I will discuss how these results combined with numerical methods may be used to prove the well known conjecture that among all triangular domains, the fundamental gap is minimized by the equilateral triangle.

04/28/09
Bing Zhu  UCSD \\ Institute for Neural Computation
Computational Modeling and Bifurcation Analysis of Fluidization Processes
AbstractFluidization processes have many important applications in industry, in particular, in chemical, fossil, and petrochemical industries where good gassolid mixing is required. Such mixing is commonly achieved through bubbles which are formed spontaneously and whose timeevolution appears to be governed by lowdimensional deterministic dynamics. A lowdimensional, computational agentbased bubble model is used to study the changes in the global bubble dynamics in response to changes in the frequency of the rising bubbles. A computationallybased bifurcation analysis shows that the collective bubble dynamics undergoes a series of transitions from equilibrium points to highly periodic orbits, chaotic attractors, and even intermittent behavior between periodic orbits and chaotic sets. Using ideas and methods from nonlinear dynamics and timeseries analysis, longterm predictions for the purpose of developing control algorithms is possible through model fitting.

04/28/09
HuanXiang Zhou  Florida State University \\ Department of Physics
Accurate calculation of binding and folding free energies by a scaled generalized Born method
AbstractThe PoissonBoltzmann equation is widely used for modeling solvation effects. The computational cost of PB has largely restricted its applications to singleconformation calculations. The generalized Born model provides an approximation at substantially reduced cost. Currently the best GB methods reproduce PB results for electrostatic solvation energies with errors at $>$ 5 to 10 kcal/mol. When two proteins form a complex, the net electrostatic contributions to the binding free energy are typically of the order of 5 to 10 kcal/mol. Similarly, the net contributions of individual residues to protein folding free energy are $<$ 5 kcal/mol. Clearly in these applications the accuracy of current GB methods is insufficient. Here we present a simple scaling scheme that allows our GB method, $GBr^6$, to reproduce PB results for binding and folding free energies with high accuracy. From an ensemble of conformations sampled from molecular dynamics simulations, five were judiciously selected for PB calculations. These PB results were used for scaling $GBr^6$. Tests on protein binding and folding show that effects of point mutations calculated by scaled $GBr^6$ are accurate to within 0.5 kcal/mol or less. This method makes it possible to incorporate conformational sampling in electrostatic modeling without loss of accuracy.

04/29/09
Paul Linden  UCSD \\ Chair, MAE; Interim director, Environment and Sustainability Initiative
Mathematical models of green buildings
AbstractThe built environment is responsible for about 30\% of greenhouse gas emissions in the US. The design of green buildings that use significantly less energy, especially for cooling, requires mathematical models that can assist architects and designers to create new designs. I will discuss one aspect  the use of natural ventilation in buildings which are cooled by using the thermal energy they acquire either through solar heating or from gains within the building from people and equipment. This kind of analysis was used to optimize the design of the new San Diego Children's Museum, among others.

04/30/09

04/30/09
Franklin Kenter  UCSD
Using Eigenvalues and Eigenvectors to Find Needles in a Haystack
AbstractFinding a needle in a haystack was once a hard problem.
However, magnets made finding that needle much easier. In the modern
age, the vast amount of information is our haystack, and a particular
piece of information is our needle, and as the title suggests,
eigenvalues and eigenvectors are our magnets. In the last decades,
many researchers have found more and more ways to use eigenvalues and
eigenvectors as our magnets to find particular the pieces of
information we are looking for. Among these include the PageRank
algorithm and spectral bipartitioning. We will give the basic theory
behind these techniques and explore some examples. 
04/30/09
Daniel Nogradi  UCSD \\ Department of Physics
Massively parallel computation on graphics hardware
AbstractIt has been recognized in the last 5 years that specialized graphics hardware can also be used for general purpose computations. The architecture of these cards is such that SIMD computations are naturally a good fit for a certain class of applications. I will outline the programming model of modern graphics cards, sketch the history of the development of the supporting software stack and if there is interest I will outline how we have implemented lattice gauge theory algorithms leading to dramatic speedup of Monte Carlo simulations.

04/30/09
Patrick Driscoll  UCSD
The Brownian semigroup and resolvent operators
May

05/04/09
Chris Tiee  UCSD
Formulating Maxwell's Equations with Differential Forms
AbstractWe continue the formulation of Maxwell's Equations in the language of differential forms. We describe how the Hodge star operator plays a role in relating the equations together, and also introduce the electromagnetic 4potential, which unifies the classical electric scalar and magnetic vector potentials into one spacetime object. We then use both these tools to recast Maxwell's Equations as a wave equation, and investigate what it means for boundary value problems.

05/05/09
Justin Roberts  UCSD
Dualisable objects and the cobordism hypothesis

05/05/09

05/05/09
Moe Ebrahimi  UCSD
Mixed finite elements for incompressible magnetohydrodynamics (MHD)

05/05/09
Jim Lin  UCSD
Finding a Thesis Advisor
Abstract\indent It is never too early for grad students to begin thinking about choosing an area of specialty and choosing among the faculty who might supervise them. One of the most important choices a graduate student will make will be choosing a thesis advisor. However, it is a process that is unlike anything that students have encountered in their undergraduate education. For this reason, we felt like it would be useful for us to run a meeting where the actual process of finding an advisor is described by students who have only recently found thesis advisors.\\
\indent How did other students find a thesis advisor? What are the key factors to consider when choosing an advisor? What do professors look for before they accept a student as their thesis student? How does finding a thesis advisor lead to finding a thesis problem? We will discuss these questions.
We will have four graduate studentsJaime Lust, Allison Cuttler, Joey Reed and Ben Wilson describe their experiences finding a thesis advisor and what happens after a thesis advisor is found.\\
\indent We will also have one faculty, Jim Lin, describe what he looks for in a graduate student before he accepts him or her as a thesis student.\\\indent All students, especially first, and second year students, are cordially invited to attend.

05/06/09
Ben Weinkove  UCSD
The KahlerRicci flow on Hirzebruch surfaces
AbstractI will discuss the metric behavior of the KahlerRicci flow on Hirzebruch surfaces assuming that the initial metric is invariant under a maximal compact subgroup of the automorphism group. I will describe how, in the sense of GromovHausdorff, the flow either shrinks to a point, collapses to $P^1$ or contracts an exceptional divisor. This confirms a conjecture of FeldmanIlmanenKnopf. This is a joint work with Jian Song.

05/07/09
Shengli Kong  UCSD
Boehm and Wilking's work on the Ricci flow on Wallach spaces

05/07/09
Daniel R. Jeske  University of California, Riverside \\ Department of Statistics
Statistical Inference Procedures for Clock Synchronization
AbstractA well known method of estimating the offset between two clocks in a data communication network involves exchanging timing messages between the clocks. Different distributions of the transmission delays in the two directions associated with the exchanged messages cause the estimator to be biased. Bootstrap biascorrection improves the estimator with respect to mean squared error. Studies on network traffic show that no single distribution adequately characterizes delays, and thus robustness of an estimator to different distribution assumptions is a critical property for an estimator to have. For common distribution assumptions for the transmission delays, the biascorrected estimator has smaller mean squared error than the uncorrected estimator. Recent studies of Internet traffic show that delay distributions can be heavytailed. Evaluation of bootstrap bias corrected estimators in the context of heavy tailed network delays leads to some surprising results. Confidence interval procedures for clock offset and a brief discussion of estimating the difference in rates between two clocks will also be given.

05/09/09
Cornelius Greither  Universitaet der Bundeswehr, Munich
Fitting ideals of class groups and of Tate modules of Jacobians

05/09/09
Yuri Zarhin  Penn State University
Families of absolutely simple hyperelliptic Jacobians
AbstractTalk time runs from 11:15 AM until 12:15 PM.

05/09/09
Ralph Greenberg  University of Washington
Galois representations with open image

05/09/09
J. K. Yu  Purdue University
Integral models of reductive groups associated to maximal bounded subgroups

05/09/09
Karl Rubin  UC Irvine
Twists of elliptic curves and Hilbert's Tenth Problem
AbstractTalk time runs from 4:455:45 PM.

05/11/09
Ryan Williams  Institute for Advanced Study
TimeSpace Lower Bounds for NPHard Problems
AbstractA fertile area of recent research has found concrete polynomial time
lower bounds for solving hard computational problems on restricted
computational models. Among these problems are Satisfiability, Vertex
Cover, Hamilton Path, MOD6SAT, and MajorityofMajoritySAT, to name
a few. The proofs of such lower bounds all follow a certain
proofbycontradiction strategy.I will survey some of the results in this area, giving an overview of
the techniques involved. If there is time I will discuss an automated
search strategy for studying these proof techniques. In particular,
the search for better lower bounds can often be turned into the task
of solving a large series of linear programming instances.
Furthermore, the limits of these proof system(s) can be understood by
analyzing the space of possible linear programs 
05/12/09
Nitu Kitchloo  UCSD
The Cobordism Hypothesis

05/12/09
Hailiang Liu  Iowa State University
Recovery of High Frequency Wave Fields from Phase Space Based
AbstractComputation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to PDEs. In this talk I will present a recovery theory of high frequency wave fields from phase space based measurements. The construction use essentially the idea of Gaussian beams, level set description in phase space as well as the geometric optics. Our main result asserts that the kth order phase space based Gaussian beam superposition converges to the original wave field in L2 at the rate of $\epsilon^{k/2n/4}$ in dimension $n$. The damage done by caustics is accurately quantified. This work is in collaboration with James Ralston (UCLA).

05/12/09
 UCSD
Finding Jobs
AbstractWe will have four panelists who have recently found jobs: Kristin Jehring, Assistant Professor, tenure track at St Mary's College, Indiana, Andy Niedermaier, Jane Street Capital, New York City, Mike Kinnally, Metron, a scientific consulting company in Reston, Virginia and Nate Eldredge, postdoc at Cornell University, Ithaca, New York.
They will describe their experiences applying for a job. Some of the questions they will answer are: How many applications should I send out? How do I prepare for an interview? What should I write in my cover letter and resume? What are important qualifications for a teaching job, postdoc job, tenure track research job and job in industry?
The discussion will be followed by a question and answer period. 
05/14/09
Shijin Zhang  UCSD
Volume growth estimate of shrinking gradient Ricci solitons

05/14/09
Masha Gordina  University of Connecticut
Gaussian type measures on infinitedimensional Heisenberg groups
AbstractThe groups in question are modeled on an abstract Wiener space. Then a
group Brownian motion is defined, and its properties are studied in
connection with the geometry of this group. The main results include
quasiinvariance of the Gaussian (heat kernel) measure, log Sobolev
inequality (following a bound on the Ricci curvature), and the Taylor
isomorphism to the corresponding Fock space. The latter map is a
version of the ItoWiener expansion in the noncommutative setting.
This is a joint work with B. Driver. 
05/14/09
Lance Small  UCSD
Divide and Conquer
AbstractNoncommutative noetherian rings will be studied
through rings of fractions. Examples will be presented and applications to baseball will be mentioned, if time permits. 
05/14/09
Brett Kotschwar  MIT
Backwardsuniqueness for the Ricci flow
AbstractI will discuss the problem of backwardsuniqueness or "uniquecontinuation" for the Ricci flow, and prove that two complete solutions $g(t)$, $\tilde{g}(t)$ to the Ricci flow on $[0, T]$ of uniformly bounded curvature that agree at $t=T$ must agree identically on $[0, T]$. A consequence is that the isometry group of a solution to the Ricci flow cannot expand in finite time.

05/14/09
Lizhen Ji  University of Michigan
Coarse Schottky Problem and Equivariant Cell Decomposition of Teichmuller Space
AbstractIn this talk, I will explain some similar results and interaction between locally symmetric spaces and moduli spaces of Riemann surfaces.
For example, let $M_g$ be the moduli space of Riemann of genus $g$, and $A_g$
be the moduli
space of principally polarized abelian varieties of dimension $g$, i.e.,
the quotient of the Siegel upper space by $Sp(2g, Z)$.
Then there is a Jacobian map $J: M_g \to A_g$, by associating to each Riemann
surface its Jacobian.The celebrated Schottky problem is to characterize the image $J(M_g).$
Buser and Sarnak viewed $A_g$ as a complete metric space and showed that $J(M_g)$ lies in a very small neighborhood of the boundary of $A_g$ as $g$ goes to infinity. Motivated by this, Farb formulated the coarse Schottky problem: determine the image of $J(M_g)$ in the asymptotic cone (or tangent space at infinity) $C_\infty(A_g)$ of $A_g$, as defined by Gromov in large scale geometry.In a joint work with Enrico Leuzinger, we showed that $J(M_g)$ is $c$dense in $A_g$ for some constant $c=c(g)$ and hence its image in the asymptotic cone $C_\infty(A_g)$ is equal to the whole cone.
Another example is that the symmetric space $SL(n,R)/SO(n)$ admits several important equivariant cell decompositions with respect to the arithmetic group $SL(n, Z)$ and hence a cell decomposition of the locally symmetric space $SL(n, Z)/SL(n, R)/SO(n)$. One such decomposition comes from the Minkowski reduction of quadratic forms (or marked lattices). We generalize the Minkowski reduction to marked hyperbolic Riemann surfaces and obtain a solution to
a folklore problem: an intrinsic equivariant cell decomposition of the Teichmuller space $T_g$ with respect to the mapping class groups $Mod_g$,
which induces a cell decomposition of the moduli space $M_g$.If time permits, I will also discuss other results on similarities between the two classes of spaces and groups.

05/14/09
Shandy Hauk  University of Northern Colorado
Video Cases of College Math Instruction Project
AbstractA national cooperative of universities is developing a collection of video case materials about college math instruction. The project goal is to create a visually rich resource for helping novice instructors build teaching skills. The purpose of the presentation is to share some of the materials, review their development, discuss their potential uses, and gather comments to inform materials redevelopment. Attendance by all department members, from those very experienced in teaching college mathematics to those with a few days experience to those with intentions to teach in the future, is heartily encouraged. Video clips come from advanced as well as introductory undergraduate mathematics teaching and learning situations.

05/19/09
Nate Eldredge  UCSD
Hypoelliptic Heat Kernel Inequalities on Htype Groups
AbstractHypoelliptic operators live in an interesting corner of the world of PDE, in which geometry plays a crucial role. Lie groups are a natural setting for the study of these operators, but even for simple examples such as the Heisenberg group, many questions remain open. I will give an overview and examples of what these objects are and how they behave, and discuss some recent results involving estimates for hypoelliptic heat kernels on
Htype groups, a class of Lie groups which generalize some of the properties of the Heisenberg group. All are welcome to attend. 
05/19/09
Nitu Kitchloo  UCSD
The cobordism hypothesis  II

05/19/09
Danny McAllaster  UCSD
Variational Integrators

05/20/09

05/21/09
Andy Niedermaier  UCSD
Tasty Tidbits from Functional Equations

05/26/09
Jonny Serencsa  UCSD
A Run Through of NavierStokes Existence and Uniqueness Results

05/26/09
Andrew Niedermaier  UCSD
Statistics on Wreath Products

05/27/09
Shengli Kong  UCSD
Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations
AbstractI will discuss a construction of ancient solutions to Ricci flow on spheres and complex projective spaces which generalize Fateev's examples on three spheres. These examples supply counterexamples to some folklore conjectures on ancient solutions of Ricci flow on compact manifolds. This a joint work with Ioannis Bakas and Lei Ni.

05/28/09
Christian Bick  UCSD
Neuroscience, just another reason to study math!?
AbstractNeural dynamics, from the dynamics of a single cell to the modeling of the activity of whole neural clusters, give rise to high dimensional dynamical systems. Unfortunately computers are too slow to solve them and math does not provide the theorems to make qualitative statements. This talk will be about models, what we can actually do and why the Fibonacci numbers keep popping up everywhere. Even when studying neural dynamics.

05/28/09
Neshan Wickramasekera  University of Cambridge
A general regularity theory for stable codimension 1 integral varifolds

05/29/09
Michael Sean Kinnally  UCSD
Stationary Distributions for Stochastic Delay Differential Equations with NonNegativity Constraints

05/29/09
Kristin Jehring  UCSD
Harmonic Functions on Walsh's Brownian Motion

05/29/09
Brett Parker  UC Berkeley
Exploded manifolds, holomorphic curves and tropical geometry
AbstractThe category of exploded manifolds is an extension of the smooth
category with a good holomorphic curve theory and a `large scale'
related to tropical geometry. I will give examples to illustrate the
usefulness of working with exploded manifolds in order to study
holomorphic curves.
Jun

06/01/09
Paul Horn  UCSD
Random Subgraphs of a Given Graph

06/02/09
Justin Roberts  UCSD
TQFTs, Costello, tangles...

06/03/09
Oded Yacobi  UCSD
An analysis of the multiplicity spaces in classical symplectic branching
AbstractWe develop a new approach to GelfandZeitlin
theory for the symplectic group $Sp(n,\mathbb{C})$. Classical GelfandZeitlin theory, concerning $GL(n,\mathbb{C})$, rests on the fact that branching from $GL(n,\mathbb{C})$ to $GL(n1,\mathbb{C})$ is multiplicityfree. Since branching from $Sp(n,\mathbb{C})$ to $Sp(n1,\mathbb{C})$ is not multiplicityfree, the theory cannot be
directly
applied to this case.Let $L$ be the $n$fold product of $SL(2,\mathbb{C})$. Our main theorem asserts that each multiplicity space that arises in the restriction of an irreducible representation of $Sp(n,\mathbb{C})$ to $Sp(n1,\mathbb{C}$, has a unique irreducible $L$action satisfying certain naturality conditions. We also given an explicit description of the $L$module structure of each multiplicity space. As an application we obtain a GelfandZeitlin type basis for the irreducible representations of $Sp(n,\mathbb{C})$.

06/04/09
Evan Fuller  UCSD
Composition/word Statistics

06/04/09
Kevin A. Heins  UCSD
Spatial Correlation of Solar Radiation Stations Using CrossSpectral Methods

06/04/09
Kathryn A. Farrell
Hamiltonian Mechanics and the Construction of Numerical Integrators

06/09/09

06/23/09
Albert Chau  University of British Columbia
Lagrangian mean curvature flow for entire Lipschitz graphs
Abstractn this joint work with Jingyi Chen and Weiyong He, we prove existence of long time smooth solutions to mean curvature flow of entire Lipschitz Lagrangian graphs. As an application, we obtain results on entire translating and selfexpanding solutions to to the Lagrangian mean curvature flow.

06/29/09
Yong Wang  Department of Statistics, University of Auckland \\ New Zealand
Fast Computation for Fitting Nonparametric and Semiparametric Mixture Models
AbstractNonparametric and semiparametric mixture models are valuable
tools for solving many nasty problems when a population is
heterogeneous. While the maximum likelihood approach is straightforward,
its computation has long been known as being difficult, if not
intractable, due to the estimation of a distribution function defined on
an infinitedimensional space. In this talk, I will describe some fast
algorithms that I recently developed for fitting these models; present
the results of their use in several applications, including the
overdispersion problem, simultaneous hypothesis testing, the
NeymanScott problem and mixed effects models; and discuss some
implementation issues using R. 
06/30/09

06/30/09
Benjamin James Cooper  UCSD
3Dimensional Topological Field Theory and Harrison Homology
Jul

07/02/09
Nolan Wallach  UCSD
Hidden subgroups in $ax+b$ groups revisited
Aug

08/18/09
Cheikh Birahim Ndiaye  University of Tuebingen
A fourthorder uniformization theorem for 4manifolds with boundary
AbstractIn this talk, we will discuss the problem of finding conformal metrics
with constant Qcurvature on a given compact four dimensional Riemannian
manifold (M,g) with boundary. This will be equivalent to solving a fourth
order nonlinear elliptic boundary value problem with boundary condition
given by a thirdorder pseudodifferential operator, and homogeneous Neumann
condition which has a variational structure. However when some conformally
invariant quantity associated to the problem is large, the EulerLagrange
functional associated is unbounded from below, implying that we have to
find critical points of saddle type. We will show how the search of saddle
points leads naturally to consider a new barycentric set of the manifold.
Sep

09/08/09
Frank Kelly  University of Cambridge
Brownian Models of Congested Networks
AbstractBrownian models provide tractable highlevel descriptions
of networks in a variety of application areas. This talk will
review work in two areas: the modelling of multipath routing
in the Internet, and the design of ramp metering policies for highway networks. \\\noindent In both areas Brownian models are able to exploit the simplifications that arise in heavy traffic, and to make clear the main performance consequences of resource allocation policies.

09/09/09
Lucien Beznea  "Simion Stoilow" Institute of Mathematics of the Romanian Academy
Potential theoretical methods in the construction of measurevalued Markov branching processes
AbstractWe develop potential theoretical methods in the construction of
measurevalued branching processes. We complete results on the construction, regularity and other properties of the superprocess associated with a given right process and a branching mechanism. 
09/25/09
Jorgen Ellegaard Andersen  University of Aarhus
TQFT and quantization of moduli spaces
AbstractThe WittenReshetikhinTuraev Topological Quantum Field Theory in particular provides us with the socalled quantum representations of mapping class groups. The geometric construction of these involves geometric quantization of moduli spaces, which produced a holomorphic vector bundle over Teichm\"uller space. This bundle supports a projectively flat connection constructed by algebraic geometric techniques by Hitchin. We will present a a Toeplitz operator approximation formula for the parallel transport of the Hitchin connection. We will discuss applications of this

09/29/09
Cheikh Birahim Ndiaye  University of Tuebingen, Germany
The positive singular $\sigma_k$Yamabe problem
AbstractIn this talk, we will discuss the positive singular $\sigma_k$Yamabe
problem on $S^n\setminus \Lambda$ where $\Lambda$ is a finite set of
points of the standard sphere $S^n$, and $k$ a positive integer
verifying $0\leq 2k<n$. Geometrically, the problem is to find a complete
metric on $S^n\setminus\Lambda$ which is conformal to the standard metric
and has constant positive $\sigma_k$curvature. Analytically, it is
equivalent to finding a positive solution to a singular fullynonlinear
equation. Using asymptotic analysis combined with Fredholm theory and
contraction mapping principle, we will show how to use the disposition of
the points of $\Lambda$ to get some existence results. 
09/29/09
Glenn Tesler  UCSD
Reconstructing the Genomic Architecture of Ancestral Mammals
AbstractIn addition to frequent singlenucleotide mutations, mammalian and many other genomes undergo rare and dramatic changes called genome rearrangements. These include inversions, fissions, fusions, and translocations. Although analysis of genome rearrangements was pioneered by Dobzhansky and Sturtevant in 1938, we still know very little about the rearrangement events that produced the existing varieties of genomic architectures. Recovery of mammalian rearrangement history is a difficult combinatorial problem that I will cover in this talk. Our data sets have included sequenced genomes (human, mouse, rat, and others), as well as radiation hybrid maps of additional mammals. \\
Coauthors:
Pavel Pevzner, UCSD, Department of Computer Science and Engineering
Guillaume Bourque, Genome Institute of Singapore 
09/29/09
Jeroen Shillewaert  University of Canterbury, New Zealand \\ Department of Mathematics and Statistics
A grouptheoretic characterization of known counterexamples to the planar Kac conjecture
AbstractWe investigate pairs of Euclidean TIdomains which are isospectral but not congruent. For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [2]. The method we use dates back to T. Sunada [3] considering the problem as a geometric analogue of a method in number theory which uses Dedekind zeta functions. Counter examples to M. Kac’s conjecture sofar
can all be constructed by a certain tiling method (“transplantability”) using special linear operator groups which act 2transitively on certain associated modules. These can be represented by colored graphs, which yield information on the fixpoint structure of the groups. It is shown that if any such operator group acts 2transitively onthe associated module, no new counter examples can occur.\\\footnotesize
\noindent [1] M. KAC. Can one hear the shape of the drum?, Amer. Math. Monthly 73 (4, part 2) (1966), 1–23. \\
\noindent [2] J. MILNOR. Eigenvalues of the Laplace operators on certain manifolds, Proc. Nat. Acad. Sci. USA 51 (1964), 542. \\
\noindent [3] T. SUNADA. Riemannian Coverings and Isospectral Manifolds, Ann. Math. 121 (1980), 169–186.
Oct

10/01/09
Jason Schweinsberg  UCSD
The genealogy of branching Brownian motion with absorption
AbstractWe consider a system of particles which perform branching Brownian
motion with negative drift and are killed upon reaching zero, in the nearcritical regime where the total population stays roughly constant
with approximately N particles. We show that the characteristic time
scale for the evolution of this population is of order $(\log N)^3$,
in the sense that when time is measured in these units, the scaled
number of particles converges to a version of Neveu's continuousstate
branching process. Furthermore, the genealogy of the particles is then
governed by a coalescent process known as the BolthausenSznitman
coalescent. This validates the nonrigorous predictions by Brunet,
Derrida, Muller, and Munier for a closely related model. This is
joint work with Julien Berestycki and Nathanael Berestycki. 
10/01/09
Adrian Duane  UCSD
Kepler Walls
AbstractIn this talk, we introduce a new family of combinatorial objects called Kepler walls. Roughly speaking, a Kepler wall is a wall built of bricks in which no two bricks are adjacent, and each brick below the top row is supported by a brick in the row above. Despite their unlikely definition, Kepler walls of unrestricted width are counted by binomial coefficients, as we will see by means of a constructive bijection. We will also see connections to other interesting and wellunderstood sequences, such as the Catalan and Fibonacci numbers.

10/05/09
A. Wadsworth  UCSD
Relative Brauer groups for function fields of some curves of genus 1

10/06/09
Justin Roberts  UCSD
Introductory Meeting
Abstract\footnotesize This term's seminar will be on ``Khovanov homology and categorification''.\\
If one wants to show that some quantity takes only nonnegative integral values, one of the best ways to do so is to show that it is ``secretly'' the dimension of some vector space. ``Categorification'' is the philosophy that one should look for interesting examples of this kind of thing throughout mathematics, hoping to find that for example: \\
\begin{enumerate} \item Nonnegative integers are secretly dimensions of vector spaces
\item Integers are secretly virtual dimensions of formal differences of vector spaces (or superdimensions of supervector spaces)
\item Integer Laurent polynomials are secretly graded dimensions of Zgraded (super)vector spaces;
\item Abelian groups are secretly Grothendieck groups of additive categories \end{enumerate}
The Euler characteristic, for example, is an integervalued invariant with wonderful properties and applications. We can ``categorify'' it by viewing it as the dimension (in the second sense above) of a more powerful vectorspace valued invariant, homology. Why is homology more powerful? Because it is \textit{functorial}, capturing information about maps between spaces which the Euler characteristic can't. It's this appearance of functoriality that gives rise to the name ``categorification''.\\
In 1999 Mikhail Khovanov showed that the Jones polynomial for knots in 3space can be categorified (in the third sense above). He showed how to associate to any knot a bunch of homology groups which turn out to be strictly stronger, as topological invariants, than the Jones polynomial; moreover, they are functorial with respect to surface cobordisms in 4space between knots! The invention of Khovanov homology has not only had beautiful applications in topology (Rasmussen's proof of Milnor's conjectures about the unknotting numbers of torus knots) but also inspired a lot of work by algebraists which might ultimately explain what quantum groups ``really are''. \\
Our seminar will work through the most important papers about Khovanov homology and knot theory, beginning with those of Dror BarNatan, and if there's enough time we'll look at some of the more algebraic work too. \\
The seminar meets Tuesdays in 7218 from 10.3012. \\
I will give the first talk next Tuesday, and after that we'll try to arrange a schedule of speakers for the rest of the term. Everyone is welcome to attend and/or speak, though

10/06/09
Elizabeth Wong  UCSD
A regularized method for general quadratic programming
AbstractWe consider a quadratic programming method designed for use in a
sequential quadratic programming (SQP) method for largescale
nonlinearly constrained optimization.\\\noindent Because the efficiency of SQP methods is determined by how the
quadratic subproblem is formulated and solved, we propose an
activeset method based on inertia control that prevents
singularity in the associated KKT systems. The method is able to
utilize blackbox linear algebra software, thereby exploiting
recent advances in computer hardware. Moreover, the method makes
no assumptions on the convexity of the quadratic problems making
it particularly useful in SQP methods using exact second
derivatives. \\\noindent In addition, the method can be applied to a regularized quadratic
subproblem involving an augmented Lagrangian objective function,
eliminating the need for a fullrank assumption on the constraint
matrix. 
10/06/09
Melvin Leok  UCSD
Computational Geometric Mechanics: A Synthesis of Differential Geometry, Mechanics, and Numerical Analysis
AbstractGeometric mechanics involves the use of differential geometry and symmetry techniques to study mechanical systems. In particular, it deals with global invariants of the motion, and how they can be used to describe and understand the qualitative properties of complicated dynamical systems, without necessarily explicitly solving the equations of motion. This approach parallels the development of geometric numerical methods in numerical analysis, wherein numerical algorithms for the solution of differential equations are constructed so as to exactly conserve the invariants of motion of the continuous dynamical system.
This talk will provide a gentle introduction to the role of geometric methods in understanding nonlinear dynamical systems, and why it is important to develop numerical methods that have good global properties, as opposed to just good local behavior.

10/06/09
Adriano Garsia  UCSD
Plethystic Magics
AbstractFor over two decades we have been proving
identities involving plethystic operators
(vertex operators for some people) by
manipulations which politely could
be called ``heuristic''. But deep down I
felt them to be quite ``fishy". But referees accepted
them and we felt nevertheless confident
since we always got the right answer,
as amply confirmed by computer experimentations.
But suddenly this summer an example popped up
where our manipulations yielded a patently
false answer. Panic? Yes ... for a while.
In this talk we will present how in the end
all of this finally, and belatedly
could be made completely rigorous. 
10/08/09
Weian Zheng  University of California, Irvine
MongeKantorovich Problem
AbstractWe use a simple probability method to transform the celebrated MongeKantorovich problem in a bounded region of Euclidean plane into a Dirichlet boundary problem associated to a quasilinear elliptic equation with 0order term missing in its diffusion coefficients. Thus, we are also able to give a probability approach to the famous MongeAmpere equation, which is known to be associated to the above problem.

10/08/09
Bin Dong  UCSD
Applications of PDEs and optimization in medical image and surface processing
AbstractVariational, level set and PDE based methods and their applications in digital
image processing have been well developed and studied for the past twenty years.
These methods were soon applied to medical image processing problems.
However, the study for biological shapes, e.g. surfaces of brains or other human
organs, are still in its early stage. The bulk of this talk explores some
applications of variational, level set and PDE based methods in biological shape
processing and analysis.\\There will be three topics in this talk. The first one is on 3D brain
aneurysm capturing using level set based method, which is inspired by the technique
of illusory contours in image analysis. The second one is on multiscale
representations(MSR) of 3D shapes, which is wavelet flavored but level set and PDE based.
The third one is on Bregman iteration as a fast solver for L1minimizations and its application
to image processing problems in DNA sequencing. 
10/13/09
Lyla Fadali  UCSD
BarNatan's approach to Khovanov homology

10/13/09
Tatiana Shingel  UCSD Mathematics
Structured Approximation in a Lie Group Setting
AbstractT he talk is going to be on progress made in approximation theory of Lie
groupvalued periodic functions (loops) by socalled polynomial loops.
This
is a relatively unexplored topic within the larger area of nonlinearly
constrained approximation, which includes the study of H\"{o}lder 
10/13/09
Dragos Oprea  UCSD
An Introduction to Theta Functions
AbstractWe will discuss complex tori, and explain the role that a special class of functions, the theta functions, play in their study. I will also outline connections between theta functions and other special functions.

10/13/09
Adriano Garsia  UCSD
Plethystic Magics: II
AbstractFor over two decades we have been proving
identities involving plethystic operators
(vertex operators for some people) by
manipulations which politely could
be called ``heuristic''. But deep down I
felt them to be quite ``fishy''. But referees accepted
them and we felt nevertheless confident
since we always got the right answer,
as amply confirmed by computer experimentations.
But suddenly this summer an example popped up
where our manipulations yielded a patently
false answer. Panic? Yes ... for a while.
In this talk we will present how in the end
all of this finally, and belatedly
could be made completely rigorous. \\This talk will be a continuation of the talk from last week.

10/14/09
Anthony Licata  Stanford University
Grassmanian Geometry and sl(2) Categorification
AbstractCategorification is big business in representation theory these days,
and much of the inspiration for categorification comes from geometric
representation theory. We'll try to explain some of the geometric
inspiration for sl(2) categorification. As an application, we
describe an interesting equivalence of categories between the derived
categories of coherent sheaves on the cotangent bundle of dual
Grassmanians. \\Joint with Sabin Cautis and Joel Kamnitzer.

10/15/09
Raul Gomez  UCSD
The PeterWeyl Theorem
AbstractThe PeterWeyl theorem is one of the results that made me decide to study representation theory. In a few words it tells you how to describe the space $L^2(G)$ in terms of the representation theory of a compact group $G$.
The idea of this talk is to informally develop enough theory to state and understand this theorem and some of its consequences, and in this way motivate the study of Lie groups and their representations. No previews knowledge of the subject is assumed.

10/15/09
Yohichi Suzuki  UCSD \\ Department of Physics and Center for Theoretical Biological Physics
Singlemolecule rupture dynamics on multidimensional landscapes
AbstractSinglemolecule biophysical tools permit measurements of the mechanical response of individual biomolecules to external load, revealing details that are typically lost when studied by ensemble methods. Kramers theory of diffusive barrier crossing in one dimension has been used to derive analytical solutions for the observables in such experiments, in particular, for the force dependent lifetimes. We propose a minimalist model that captures the effects of multidimensionality of the free energy landscape on the kinetics of a singlemolecule system under constant applied force. The model predicts a rich spectrum of scenarios for the response of the system to the applied force. Among the scenarios is the conventional decrease in the lifetime with the force, as well as a remarkable rollover in the lifetime with a seemingly counterintuitive increase of the lifetime at low force followed by a decrease in the lifetime at higher forces. Realizations of each of the predicted scenario are discussed in various biological contexts. Our model demonstrates that the rollover in the lifetime does not necessarily imply a discrete switch between two coexisting pathways on the free energy landscape, and that the rollover can also be realized for a dynamics as simple as that on a single pathway with a single bound state. Our model leads to an analytical solution that reproduces the entire spectrum of scenarios, including the rollover, in the forcedependent lifetime, in terms of the microscopic parameters of the system.

10/20/09
Justin Roberts  UCSD
Lee homology and other variations on Khovanov

10/20/09
Anna Shustrova  UCSD
Modified Barrier Functions

10/20/09
John Eggers  UCSD
The Compensating Polar Planimeter
AbstractA planimeter is a device that can measure the area of a
region by tracing its perimeter. We will see how the polar planimeter
is an elegant practical example of Green's theorem. We will use
Green's theorem to elucidate various features of the polar planimeter,
such as the neutral circle and what a compensating polar planimeter
compensates for. I will show off several examples of planimeters,
including polar, rolling and radial planimeters. 
10/20/09
Sarah Mason  Wake Forest University \\ Department of Mathematics
LittlewoodRichardson Refinements Part I: Nonsymmetric and quasisymmetric functions
AbstractWe introduce a new basis for quasisymmetric functions, called
"quasisymmetric Schur functions", and provide a combinatorial rule for
the multiplication of a quasisymmetric Schur function by a Schur
function. We extend this approach to develop similar multiplication
rules for Demazure characters and for Demazure atoms. This is joint
work with Jim Haglund, Kurt Luoto, and Steph van Willigenburg. 
10/22/09
Bo Yang  UCSD
Tian's result on approximating polarized Kaehler metric on algebraic manifolds
AbstractI will talk about a main theorem in Tian's JDG paper ``On a set
of polarized Kaehler metrics on algebraic manifolds''. A crucial
ingredient is to use Hormander's estimates to construct so called peak
sections (which has energy concentration at a isolated point and
prescribed polynomial growth order around that point). 
10/22/09
Montgomery Taylor  UCSD
ZeroDivisor Graphs
AbstractWe shall investigate $\gamma(R)$, the zerodivisor graph of a commutative ring $R$ (where $0 \ne 1$). Specifically, if $R$ is the given ring, let $\gamma(R) = (V,E)$ with $V = Z(R)$ and $E=\{ \{x,y\}  xy=0\}$. We will show elementary properties of $\gamma(R)$ and restrict our attention to graphs with finitely many vertices.

10/22/09
Eunjung Kim  University of Notre Dame \\ Department of Mathematics
Multiscale Biomechanical Models for Biological Soft Tissue
Abstract\footnotesize
Articular cartilage is a resilient soft tissue that supports load joints at the knee, shoulder and hip. Cartilage is primarily comprised of interstitial water (roughly 80\% by volume) and extracellular matrix (ECM). Cells called chondrocytes are dispersed through ECM and maintain and regenerate the tissue. Chondrocytes are surrounded by a narrow layer called pericellular matrix (PCM), which is believe to be important for modulating the biomechanical environment of chondrocyte. In this study, computational models will be presented to analyze the multiscale micromechanical environment of chondrocytes.\\
Firstly, we will discuss transient finite element method (FEM) to model linear biphasic mechanics of a single cell within cartilage layer under cyclic loading. The FEM model was employed to analyze the effects of frequency on mechanical variables in cellular environment under macroscopic loading at 1\% strain and in the frequency range 0.01 0.1 Hz. In this frequency range, intracellular axial strains exhibited up to a tenfold increase in magnitude relative to 1\% applied strain. The dynamics of strain amplification exhibited a twoscale response that was highly dependent on ratios of typical time scales in the model, such as the loading period, gel diffusion times for the cell, the PCM and the ECM. In conjunction with strain amplification, solid stress in the surrounding ECM was reduced by up to 35\%. We propose here that the computational model developed in this study has potential application in correlating mechanical variables in the cellular microenvironment to biosynthetic responses induced by cyclic loading of native cartilage or engineered cellgel constructs.\\
Secondly, we will discuss the formulation, implementation and application of multiscale axisymmetric boundary element method (BEM) for simulating in situ deformation of chondrocyte and the PCM in states of mechanical equilibrium. The BEM was employed to conduct a multiscale continuum model to determine linear elastic properties of the PCM in situ. Taken together with previous experimental and theoretical studies of cellmatrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte. \\
This is joint work with Mansoor Haider (NCSU), and our experimental colleague, Farshid Guilak (Duke).

10/22/09
Sebastian CasainaMartin  University of Colorado at Boulder
Birational geometry of the moduli space of genus four curves
AbstractIn addition to the DeligneMumford compactification for the moduli space of genus four curves, there are a number of additional compactifications that arise naturally. In this talk I will discuss joint work with Radu Laza where we compare some of these spaces. The description we obtain is similar to that for genus three curves (work of HyeonLee), as well as to some previous results we have for the moduli space of cubic threefolds.

10/23/09
Jitse Niesen  University of Leeds, UK \\ Department of Applied Mathematic
Exponential integration of large systems of ODEs
AbstractExponential integrators are methods for the solution of ordinary differential equations which use the matrix exponential in some form. As the solution to linear equations is given by the exponential, these methods are well suited for stiff ordinary differential equations where the stiffness is concentrated in the linear part. Such equations arise when semidiscretizing semilinear differential equations. The biggest challenge for exponential integrators is that we need to compute the exponential of a matrix. If the matrix is not small, as is the case when solving partial differential equations, then an iterative method needs to be used. Methods based on Krylov subspaces are a natural candidate. I will describe the efforts of Will Wright (La Trobe University, Melbourne) and myself to implement such a procedure and comment on our results.

10/27/09

10/27/09
Ryan Szypowski  UCSD
Numerical Solution of TimeDependant PDEs
AbstractPartial differential equations (PDEs) can be used to model numerous
physical processes, from steadystate heat distribution to the
formation of black holes. When the solution changes over time,
special techniques and considerations must be taken for their accurate
solution. In this talk, I will briefly introduce the concepts,
discuss a few of the concerns, and show some numerical results from
simple model problems. 
10/27/09
Sarah Mason  Wake Forest University \\ Department of Mathematics
LittlewoodRichardson Refinements Part II: Corollaries and applications
AbstractWe describe several corollaries of the LittlewoodRichardson refinements, including a method for multiplying two Schur functions with different numbers of variables and expanding the result as a sum of key polynomials. We use interactions between Schur functions and quasisymmetric Schur functions to prove a conjecture of Bergeron and Reutenauer. We show that their conjectured basis is indeed a basis for the quotient ring of quasisymmetric functions by symmetric functions, which also provides a combinatorial proof of Garsia and Wallach's results about the freeness and dimension of QSym/Sym. This is joint work with Aaron Lauve.

10/28/09
Wesley K. Thompson  UCSD
A StimulusLocked Vector Autoregressive Model for EventRelated fMRI
AbstractNeuroscientists have become increasingly interested in exploring
dynamic
relationships among brain regions. Such a relationship, when directed from
one region toward another, is denoted by ``effective connectivity.'' An fMRI
experimental paradigm which is
wellsuited for examination of effective connectivity is the slow
eventrelated design.
This design presents stimuli at sufficient temporal spacing for determining
withintrial
trajectories of BOLD activation. However, while several analytic methods for
determining
effective connectivity in fMRI studies have been devised, few are adapted to
the
characteristics of eventrelated designs, which include nonstationary BOLD
responses and nesting of responses within trials and subjects.
We propose a model tailored for exploring effective connectivity
of multiple brain regions in eventrelated fMRI designs  a semiparametric
adaptation of vector autoregressive (VAR) models, termed "stimuluslocked
VAR"
(SloVAR). Connectivity coefficients vary as a function of time
relative to stimulus onset, are regularized via basis expansions, and vary
randomly across subjects. SloVAR obtains flexible, datadriven estimates of
effective
connectivity and hence is useful for building connectivity models when prior
information
on dynamic regional relationships is sparse. Indices derived from the
coefficient estimates can also be used to relate effective connectivity
estimates
to behavioral or clinical measures. We demonstrate the SloVAR model
on a sample of clinically depressed and normal controls, showing that
early but not late corticoamygdala connectivity appears crucial to
emotional control and
early but not late corticocortico connectivity predicts depression severity
in the depressed group, relationships that would have been missed in a more
traditional VAR analysis. 
10/28/09
Qingtao Chen  University of Southern California
Quantum Invariants of Links

10/29/09
Shijin Zhang  UCSD
Ricci flow coupled with harmonic map flow  Reto Muller's work
AbstractReto Muller investigated a new geometric flow which consists
of a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $\phi$ from $M$ to some closed target closed manifold $N$, given by $\frac{\partial}{\partial t} g =  2 Ric + 2 \alpha \nabla \phi \bigotimes \nabla \phi, \frac{\partial}{\partial t}\phi = \tau_{g}\phi $, where $\alpha$ is a positive coupling constant. This new flow shares many good properties with the Ricci flow. 
10/29/09
Katharine Shultis  UCSD
GelfandKirillov Dimension and the Bergman Gap Theorem
AbstractWe will define useful definitions of growth on an algebra. In particular, we will consider GelfandKirillov (GK) dimension. After stating some nice properties of GK dimension of algebras, we will sketch a combinatorial proof of the Bergman Gap Theorem.

10/29/09
Bo Hu  UCSD Department of Physics
Stochastic Information Processing and Optimal Design in Eukaryotic Chemotaxis
AbstractChemotaxis is characterized by the directional cell movement following external chemical gradients. It plays a crucial role in a variety of biological processes including neuronal development, wound healing and cancer metastasis. Ultimately, the accuracy of gradient sensing is limited by the fluctuations of signaling components, e.g. the stochastic receptor occupancy on cell surface. We use concepts and techniques from interrelated disciplines (statistics, information theory, and statistical physics) to model the stochastic information processing in eukaryotic chemotaxis. Specifically, we address the following issues:
\begin{enumerate} \item What are the physical limits of the gradient estimation? \\ \item How much information can be reliably gained by a chemotaxing cell? \\ \item How to optimize the chemotactic performance? \\ \end{enumerate}
Through answering those questions, we expect to derive extra insights for general biological signaling systems.

10/29/09
Greg Blekherman  Virginia Tech
Nonnegative Polynomials and Sums of Squares: Real Algebra meets Convex Geometry
AbstractA multivariate real polynomial is nonnegative if its value is at least zero for all points in $\mathbb{R}^n$. Obvious examples of nonnegative polynomials are squares and sums of squares. What is the relationship between nonnegative polynomials and sums of squares? I will review the history of this question, beginning with Hilbert's groundbreaking paper and Hilbert's 17th problem. I will discuss why this question is still relevant today, for computational reasons, among others. I will then discuss my own research which looks at this problem from the point of view of convex geometry. I will show how to prove that there exist nonnegative polynomials that are not sums of squares via ``naive" dimension counting. I will discuss the quantitative relationship between nonnegative polynomials and sums of squares and also show that there exist convex polynomials that are not sums of squares.

10/30/09
Swatee Naik  University of Nevada, Reno
Classical Knot Concordance
AbstractKnots are embeddings of circles in the three dimensional sphere. We will discuss an equivalence relation called knot concordance and the group of equivalence classes under connect sum

10/30/09
Swatee Naik  University of Nevada, Reno
Knot Concordance Group
AbstractWe will discuss the structure of the knot concordance group, finite order concordance classes and open problems in the area.
Nov

11/02/09
Alexander Mikhalev  Moscow State University
Multiplicative properties of rings

11/03/09
Ben Hummon  UCSD
Khovanov homology and surfaces in 4space

11/03/09
Jiawang Nie  UCSD
Regularization Methods for Sum of Squares Relaxations in Large Scale Polynomial Optimization
AbstractWe study how to solve sum of squares (SOS) and Lasserre's
relaxations for large scale
polynomial optimization. When interiorpoint type methods are used,
typically only small
or moderately large problems could be solved. This paper proposes the
regularization
type methods which would solve significantly larger problems. We first
describe these
methods for general conic semidefinite optimization, and then apply
them to solve large
scale polynomial optimization. Their efficiency is demonstrated by
extensive numerical
computations. In particular, a general dense quartic polynomial
optimization with 100
variables would be solved on a regular computer, which is almost
impossible by applying
prior existing SOS solvers. 
11/03/09
Sarah Mason  UCSD / Wake Forest University
Symmetric Venn diagrams and partially ordered sets
AbstractVenn diagrams are tools used to represent relationships among
sets. They are easy to understand but can be difficult to draw if they
involve more than three sets. The quest for a method to construct symmetric
Venn diagrams has led to some interesting theorems about partially ordered
sets. We describe several of these theorems, their relationship to Venn
diagrams, and a conjecture that unifies this research. 
11/04/09
Andrea Young  University of Arizona
Ricci YangMills solitons on nilpotent Lie groups
AbstractThere has been much recent progress in the study of Ricci solitons on nilpotent and solvable Lie groups. In this talk, I will define the Ricci YangMills flow which is related to the Ricci flow. I will also define Ricci YangMills solitons, which are generalized fixed points of the Ricci YangMills flow. These metrics are related to Ricci solitons; however, they are defined on principal Gbundles and are designed to detect more of the bundle structure. On nilpotent Lie groups, one can say precisely in what sense Ricci YangMills solitons are related to Ricci solitons. I will provide examples of 2step nilpotent Lie groups that admit Ricci YangMills solitons but that do not admit Ricci solitons. This is joint work with Mike Jablonski.

11/05/09
Todd Kemp  UCSD, MIT 20092010
Chaos and the Fourth Moment
AbstractThe Wiener Chaos is a natural orthogonal decomposition of the $L^2$ space of a Brownian motion, naturally associated to stochastic integration theory; the orders of chaos are given by the range of multiple WienerIto integrals.
In 2006, Nualart and collaborators proved a remarkable central limit theorem in the context of the chaos. If $X_k$ is a sequence of $n$th WienerIto integrals (in the $n$th chaos), then necessary and sufficient conditions that $X_k$ converge weakly to a normal law are that its (second and) fourth moments converge  all other moments are controlled by these.
In this lecture, I will discuss recent joint work with Roland Speicher in which we prove an analogous theorem for the empirical eigenvalue laws of highdimensional random matrices.

11/05/09
Christopher Tiee  UCSD
Understanding Analysis by Any Means Possible
AbstractThe concept of average is highly useful (and much maligned) concept in all of mathematics and in life. However, few people stop to think about what an average really \emph{is}. As it turns out, it is a very important theoretical concept in mathematics, and it isn't just something that helps one lie with statistics. It is really the heart of measure and integration theory. In this talk we'll learn how measure theory and integration unifies various different kinds of averages, and one big result: Jensen's inequality, and its applications to relating more exotic means to one another.

11/05/09
Arijit Maitra  UCSD \\ Department of Nanoengineering
Model of Dynamic SingleMolecule Force Spectroscopy That Harnesses Both Loading Rates and Device Stiffness
Abstract\footnotesize Singlemolecule force spectroscopy experiments involve imposition of controlled forces at the single molecule level and observing the corresponding mechanical behavior of the molecule. The molecular resistance to deformation can be utilized for studying transition pathways of molecules in terms of energy, time scales and even number of transition states. These have found applications in a wide variety of problems, for instance, to understand foldingunfolding dynamics of biomolecules, ligandreceptor binding, transcription of DNA by RNA polymerase, motion of molecular motors to name a few.
Existing analyses of force measurements rely heavily on theoretical models for reliable extraction of kinetic and energetic properties. Despite significant advances, there remain gaps in fully exploiting the experiments and their analyses. Specifically, the effect of pulling device stiffness or compliance has not been comprehensively captured. Hence, the best models for extracting molecular parameters can only be applied to measurements obtained from soft pulling devices (e.g., optical tweezers) and result in welldocumented discrepancies when applied to stiff devices (e.g., AFM). This restriction makes pulling speed the only control parameter in the experiments, making reliable extraction of molecular properties problematic and prone to error. \\Here, we present a onedimensional analytical model derived from physical principles for extracting the intrinsic rates and activation free energies from rupture force measurements that is applicable to the entire range of pulling speeds and device stiffnesses. The model therefore is not restricted to the analyses of force measurements performed with soft pulling devices only. Further, the model allows better design of experiments that specifically exploits device stiffness as a control parameter in addition to pulling speed for a more reliable estimation of energetic and kinetic parameters. The model also helps explain previous discrepancies noted in rupture forces measured with devices of different effective stiffnesses and provides a framework for modeling other stiffnessrelated issues in singlemolecule force spectroscopy.

11/05/09
Arijit Maitra  UCSD \\ Department of Nanoengineering
Model of Dynamic SingleMolecule Force Spectroscopy That Harnesses Both Loading Rates and Device Stiffness
Abstract\footnotesize Singlemolecule force spectroscopy experiments involve imposition of controlled forces at the single molecule level and observing the corresponding mechanical behavior of the molecule. The molecular resistance to deformation can be utilized for studying transition pathways of molecules in terms of energy, time scales and even number of transition states. These have found applications in a wide variety of problems, for instance, to understand foldingunfolding dynamics of biomolecules, ligandreceptor binding, transcription of DNA by RNA polymerase, motion of molecular motors to name a few.
Existing analyses of force measurements rely heavily on theoretical models for reliable extraction of kinetic and energetic properties. Despite significant advances, there remain gaps in fully exploiting the experiments and their analyses. Specifically, the effect of pulling device stiffness or compliance has not been comprehensively captured. Hence, the best models for extracting molecular parameters can only be applied to measurements obtained from soft pulling devices (e.g., optical tweezers) and result in welldocumented discrepancies when applied to stiff devices (e.g., AFM). This restriction makes pulling speed the only control parameter in the experiments, making reliable extraction of molecular properties problematic and prone to error. \\Here, we present a onedimensional analytical model derived from physical principles for extracting the intrinsic rates and activation free energies from rupture force measurements that is applicable to the entire range of pulling speeds and device stiffnesses. The model therefore is not restricted to the analyses of force measurements performed with soft pulling devices only. Further, the model allows better design of experiments that specifically exploits device stiffness as a control parameter in addition to pulling speed for a more reliable estimation of energetic and kinetic parameters. The model also helps explain previous discrepancies noted in rupture forces measured with devices of different effective stiffnesses and provides a framework for modeling other stiffnessrelated issues in singlemolecule force spectroscopy.

11/06/09
A.A. Mikhalev  Moscow State University
Primitive elements in the free nonassociative algebra: algorithms

11/06/09
Nolan Wallach  UCSD
QuoternionKaehler manifolds

11/09/09
S. K. Jain  Ohio University
Rings determined by Properties of its Cyclic Modules

11/09/09
Valentino Tosatti  Columbia University
Collapsing of Ricciflat metrics
AbstractWe are interested in the behaviour of Ricciflat Kahler metrics on a compact CalabiYau manifold, with Kahler classes approaching the boundary of the Kahler cone. The case when the volume approaches zero is especially interesting since the corresponding complex MongeAmpere equation degenerates in the limit. If the CalabiYau manifold is the total space of a holomorphic fibration, the Ricciflat metrics collapse to a metric the base, which `remembers' the fibration structure.

11/10/09
Justin Roberts  UCSD
Kuperberg's webs, representation categories, and SL(3) Khovanov homology

11/10/09
Michael Ferry  UCSD
Line Search Algorithms for ProjectedGradient QuasiNewton Methods
AbstractWe briefly survey line search algorithms for unconstrained
optimization.
Next, we consider the search direction and line search strategies used
in
several algorithms that implement a quasiNewton method for simple
bounds,
including algorithm LBFGSB. In this context, we discuss two
currentlyused line search algorithms and introduce a new method meant
to
combine the best properties of two different strategies. We present a
modified LBFGSB method using the new line search and demonstrate its
significant performance gains by numerical tests using the CUTEr test
set. 
11/10/09
Juhi Jang  Courant Institute
On the Hilbert expansion of the Boltzmann equations
AbstractThe asymptotic expansions to the Boltzmann equations provide a clue of the
connection from kinetic theory to fluid mechanics.
The Hilbert expansion turns out to be useful to verify compressible fluid
limits. As its applications, we rigorously establish the compressible Euler and
acoustic limits from the Boltzmann equation and the EulerPoisson limit from
the VlasovPoissonBoltzmann system. Moreover, we prove a globalintime
convergence for a repulsive EulerPoisson flow for irrotational monatomic gas. 
11/10/09
Dan Rogalski  UCSD
The Quaternions
AbstractThe quaternions form an interesting and useful number system which is a (noncommutative!) extension of the complex numbers. We define the quaternions and give some of the famous history surrounding Hamilton's discovery of them. We describe some applications of quaternions to geometry and algebra.

11/10/09
Kevin Woods  Oberlin College
Solving Lattice Point Problems Using Rational Generating Functions
AbstractAs an example, consider the following problem. Given positive
integers $a_1,…,a_d$ that are relatively prime, let S be the set of
integers that can be written as a nonnegative integer combination of
these $a_i$. We can think of the $a_i$ as denominations of postage stamps
and S as the postal rates that can be paid exactly using these
denominations. What can we say about the structure of this set, S? What
is the largest integer not in S (called the Frobenius number)? How many
positive integers are not in S?We attack these problems using the generating function $f_S(x)$, defined
to be the sum, over all elements s of S, of the monomials $x^s$. We will
build up the general theory of computing generating functions – for
this and other problems – and then use these generating functions to
answer questions we’re interested in. We will approach these problems
from an algorithmic perspective: what can we do in polynomial time? 
11/12/09
Lyla Fadali  UCSD
Being A Good Scout, Knowing Your Knots, and the Jones Polynomial
AbstractIn 1990, Jones received a Fields Medal, in part, for his work on knots and knot invariants. In particular, he developed what is now known as the Jones polynomial which can serve to distinguish two knots from one another. In this talk, we introduce the Jones polynomial and its basic properties and how it can be helpful to scouts who need to know their knots.

11/12/09
Immanuel Kalcher  Technical University Munich \\ Physics Department
Modeling ionspecific correlations in bulk and confinement
Abstractonspecific effects are ubiquitous in nature and have relevance in colloidal
science, electrochemistry, and geological and biological physics. The molecular
origin and the coarsegrained modeling of these effects are still widely unexplored.
In this talk we attempt to give more molecular insight into the individual
correlations in aqueous electrolyte systems which give rise to the ionspecific
behavior in bulk (e.g., the osmotic pressure) or in confinement (e.g., between
colloidal or biological surfaces). Particularly, we present a nonlocal
PoissonBoltzmann theory, based on classical density functional theory,
which captures and rationalizes ionspecific excludedvolume correlations
(the 'size effect') in dense electrolytes and may help understanding the
restabilization of proteins, clays, and colloids at high salt concentrations.
The importance of electrostatic correlations at low dielectric constants is
briefly discussed. 
11/13/09
I. Kryliuk  De Anza College
Selfsimilar algebras

11/17/09
Joey Reed  UCSD
Electrical Impedance Tomography
Abstractlectrical Impedance Tomography (EIT) is a medical imaging
technique which attempts to
find conductivity inside the human body.
Mathematically speaking, EIT is an inverse
problem. In inverse problems, experimental data is
used to approximate some property
(or control) of the system of interest. For EIT,
this experimental data is electric potential
on the body's surface. One big concern with EIT is
that it is a highly illposed problem.
In our context, this means that the conductivity is
highly dependent on experimental
noise.
In this talk I will describe the mathematical
model used for the forward problem of EIT.
The inverse problem will then be described as a
constrained least squares problem. 
11/17/09
Ery AriasCastro  UCSD
Detection of an Abnormal Cluster in a Network
AbstractWe consider the model problem of detecting whether or not in a given sensor network, there is a cluster of sensors which exhibit an unusual behavior. Formally, suppose we are given a set of nodes and attach a random variable to each node which represent the measurement that a particular sensor transmits. Under the normal circumstances, the variables have a standard normal distribution. Under abnormal circumstances, there is a cluster (subset of nodes) where the variables now have a positive mean. The cluster is unknown but restricted to belong to a class of interest, for example discrete squares.\\
We also address surveillance settings where each sensor in the network transmits information over time. The resulting model is similar, now with a time series is attached to each node. We consider some wellknown examples of growth models, including cellular automata used to model epidemics.\\
In both settings, we study best possible detection rates under which no test works. We do so for a variety of cluster classes. In all the situations we consider, we show that the scan statistic, by far the most popular method in practice, is nearoptimal.\\
Joint work with Emmanuel Candes (Stanford) and Arnaud Durand (Universit$\mathrm{\acute{e}}$ Paris XI)

11/18/09
Jie Qing  UC Santa Cruz
Scattering on conformally compact Einstein manifolds
AbstractI will talk about the scattering operators on conformally compact Einstein manifolds based on the work of Graham and Zworski. A conformally compact Einstein manifold comes with a conformal manifold as its conformal infinity. I will show scattering operators, as spectral property of the bulk space, in many ways are related to global conformal property of the infinity. I will in particular talk about a recent joint work with Colin Guillarmou on the relation of the location of real scattering poles and the Yamabe constant of the conformal infinity.

11/19/09
Matus Telgarsky  UCSD, Department of Computer Science
Central Binomial Tail Bounds
AbstractAn alternate form for the binomial tail is presented, which leads to a variety of bounds for the central tail. A few can be weakened into the corresponding Chernoff and Slud bounds, which not only demonstrates the quality of the presented bounds, but also provides alternate proofs for the classical bounds.

11/19/09
Alex Eustis  UCSD
Estimating Markov Chains with Differential Equations
AbstractTwo types of dynamical system are differential equations and Markov chains, representing continuous deterministic systems and discrete random systems respectively. For a Markov chain in which the jumps are ``small and frequent,'' the individual random jumps can average out to a ``drift'' as in a firstorder differential equation. We'll explore a couple of general results of this type and do a couple examples, largely following a paper by Darling and Norris.

11/19/09
Andre Minor  UCSD
CR embeddings into higher dimensional spheres

11/19/09
Jim Lin  UCSD
Finding a Thesis Advisor
AbstractOne of the most important choices a graduate student will make will be choosing a thesis advisor. It is never too early for students to begin thinking about choosing an area of specialty and choosing among the faculty who might supervise them.
How did other students find a thesis advisor? What are the key factors to consider when choosing an advisor? What do professors look for before they accept a student as their thesis student? How does finding a thesis advisor lead to finding a thesis problem? We will discuss these questions.
We will have four graduate studentsRaul Gomez, Mike Scullard, Michael Ferry and Kevin McGown describe their experiences finding a thesis advisor and what happens after a thesis advisor is found.
We will also have one faculty, Jim Lin, describe what he looks for in a graduate student before he accepts him or her as a thesis student.
All students, especially first, second and third year students, are cordially invited to attend. 
11/19/09
Herbert Heyer  Univ. Tuebingen, Germany
Hypergroup stationarity of random fields
AbstractTraditionally weak stationarity of a random field $\{X(t) : t\in \mathbf{T}\}$ over an index space $\mathbf{T}$ is defined with respect to a translation operation in $\mathbf{T}$. But this classical notion of stationarity does not extend to related random fields, as for example to the field of averages of $\{X(t): t\in \mathbf{T}\}$. In order to equip this latter field with a stationarity property one introduces a generalized translation in $\mathbf{T}$ which arises from a generalized convolution structure in the space $M^b(\mathbf{T})$ of bounded measures on $\mathbf{T}$. There are two fundamental constructions providing such (hypergroup) convolution structures on the index spaces $\mathbf{Z}_+$ and $\mathbf{R}_+$, in terms of polynomial sequences and families of special functions, respectively.\\
In the present talk emphasis will be put on polynomially stationary random fields $\{X(n): n\in\mathbf{Z}_+\}$ which were studied for the first time by R.~Lasser and M.~Leitner about 20 years ago. In the meantime the theory has developed interesting applications such as regularization, moving averages and prediction.\\
For squareintegrable radial random fields over graphs, J.P.~Arnaud has coined a notion of stationarity which yields spectral and Karhunen type representations.
These fields are related to polynomially stationary random fields over $\mathbf{Z}_+$, where the underlying polynomial sequence generates the CartierDunau convolution structure in $M^b(\mathbf{Z}_+)$. An analogous approach related to special function stationarity of random fields over $\mathbf{R}_+$ seems promising, but requires further progress. 
11/24/09
Hans Wenzl  UCSD
Quantum groups and categorification

11/24/09
Jacob Sterbenz  UCSD
Introduction to some problems in linear and nonlinear waves
AbstractThis is an overview talk for students on problems in the field of nonlinear wave equations. We'll
first introduce several models from classical field theory,
and then discuss some open problems and current techniques
for approaching them. The focus of this and future
seminars will be on asymptotic
stability problems and decay estimates. 
11/24/09
Xun Jia and Chunhua Men  UCSD \\ School of Medicine, Department of Radiation Oncology
Some Optimization Problems in Cancer Radiotherapy
Abstract\small This talk will focus on the following two problems.
\begin{enumerate}\item Cone beam computed tomography (CBCT) reconstruction.
CBCT has been extensively studied for many
years. It is desirable to reconstruct the CBCT
image with as few xray projections as possible in
order to reduce radiation dose. In this talk, we
present our recent work on an iterative CBCT
reconstruction algorithm. We consider a cost
function consisting of a data fidelity term and a
totalvariance regularization term. A
forwardbackward splitting algorithm is used to
minimize the cost function efficiently. We test
our reconstruction algorithm in a digital patient
phantom and the reconstruction can be achieved
with 30 CBCT projections. Our algorithm can also
be applied in 4D CBCT reconstruction problem. A
proposed temporal regulation algorithm for 4DCBCT
reconstruction will also be discussed.\item Treatment plan optimization.
When beam of radiation passes through a patient,
they may kill both cancerous and normal cells, so
the goal of the treatment is to kill the tumor (by
delivering the prescribed dose to it), while
sparing the organsatrisk (by minimizing the dose
to it). We define our objective function as a
penaltybased oneside quadratic function based on
the dose received by each voxel. Overdosing
penalty is given to all voxles, while underdosing
penalty is only given to tumor voxels. The
decision variables can be intensity of each beam
bixel (IMRT Fluence Map Optimization), intensity
and shape of each beam aperture (IMRT Direct
Aperture Optimization), or aperture shape and
intensity in each beam angle (VMAT Optimization),
depending on various radiation techniques and/or
models.
\end{enumerate}
The reconstruction process and one of treatment
plan optimization models have been implemented on
Nvidia CUDA platform on GPU and a high computing
efficiency has been achieved. 
11/24/09
Benjamin Weinkove  UCSD
Convergence of metric spaces
AbstractA metric space is a set together with a notion of distance. An example would be 3space with our usual definition of distance, but there are lots of examples which could be quite abstract. Suppose we're given two such spaces: how far apart are they? Does this even make sense? Is there a welldefined notion of the distance between abstract metric spaces? Can a sequence of abstract metric spaces converge? We will discuss these questions in relation to some recent research on curvature flows and geometry.

11/24/09
Gregg Musiker  MIT \\ Department of Mathematics
Linear Systems on Tropical Curves
AbstractA tropical curve is a metric graph with possibly unbounded edges, and
tropical rational functions are continuous piecewise linear functions
with
integer slopes. We define the complete linear system $D$ of a divisor $D$
on
a tropical curve analogously to the classical counterpart. Due to work
of
Baker and Norine, there is a rank function $r(D)$ on such linear systems,
as well a canonical divisor $K$. Completely analogous to the classical
case, this rank function satisfies RiemannRoch and analogues of
RiemannHurwitz.After an introduction to these tropical analogues, this talk will
describe
joint work with Josephine Yu and Christian Haase investigating the
structure of $D$ as a cell complex. We show that linear systems are
quotients of tropical modules, finitely generated by vertices of the
cell
complex. Using a finite set of generators, $D$ defines a map from the
tropical curve to a tropical projective space, and the image can be
extended to a parameterized tropical curve of degree equal to $\mathrm{deg}(D)$.
The
tropical convex hull of the image realizes the linear system $D$ as an
embedded polyhedral complex. 
11/30/09
Ljudmila Kamenova  Stony Brook
HyperKaehler fibrations
AbstractWe consider hyperKaehler manifolds of complex dimension 4 which are fibrations. It is known that the fibers are abelian varieties and the base is $\mathbb P^2$. We assume that the general fiber is isomorphic to a product of two elliptic curves. Our result is that such a hyperKaehler manifold is deformation equivalent to a Hilbert scheme of two points on a K3 surface.
Dec

12/01/09
Hans Wenzl  UCSD
Quantum groups and categorification  II

12/01/09
Hieu Nguyen  UCSD
Adaptive and Fully Automatic hpAdaptive Finite Elements
AbstractIn this talk, we study how to use gradient/derivative recovery techniques to formulate error estimate and error indicator for padaptive FEMs, where elements are allowed to have variable degrees. The study also suggests an approach to implement a fully automatic hpadaptive FEM. In this approach, the
decision on whether to refine a given element into two child elements (hrefinement) or increase its degree (prefinement) is made heuristically purely on information from error estimate. Several numerical results will be presented to show the efficiency of the methods. 
12/01/09
Jacob Sterbenz  UCSD
Decay Estimates on Flat Spacetimes
AbstractIn this talk we'll focus on various dispersive estimates for the wave equation on Minkowski Space.

12/01/09
Jeff Rabin  UCSD
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
AbstractThe title of this talk is the same as that of an influential article published in 1960 by the physicist and mathematician Eugene Wigner. Wigner's thesis is that mathematics is obviously an effective tool in the sciences (especially physics), but it is unreasonably so: much more successful at describing natural laws than could reasonably be expected. He concludes, ``The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.'' I will survey the evidence that led him to this conclusion, examine some later attempts to explain this miracle, and hint at my own viewpoint. I hope to hear yours as well.

12/01/09

12/03/09
Janko Gravner  University of California, Davis
Random threshold growth and related models
AbstractThe occupied set grows by adding points x which have at least theta already occupied points in their neighborhoods. Such ``threshold growth'' models are interesting in many contexts. For growth on an integer lattice, explicitly computable approximations can be developed when the neighborhood range is large. Other cases will also be briefly addressed.

12/03/09
Dr. Shuangliang Zhao  UC Riverside  Chemical Engineering
Density functional theory for solvation in molecular solvents
AbstractSolvation is ubiquitous in experiments. In this talk, an accurate classical density functional theory (DFT) is presented for predicting the microscopic structure and thermodynamic properties of an arbitrary molecule solvated in a molecular solvent. The novel freeenergy functional is constructed in terms of solvent density which depends on position and orientation of solvent molecule. The key input is the inhomogeneous position and orientation dependent solvent direct correlation function, and this direct correlation function is calculated by the “homogeneous reference fluid approximation”, namely in terms of the direct correlation function of the pure solvent system (the cfunction).
Towards precise prediction, we propose the following strategy: we first perform MD simulations of the pure solvent system, and then sample over many solvent configurations so as to compute the position and angledependent twobody distribution functions (the hfunction). Subsequently applying the socalled molecular OrnsteinZernike relation, we obtain the corresponding direct correlation function, which serves as input for the free energy functional. In the presence of a given molecular solute, which provides the external potential, this functional can be minimized with respect to water density , using a 3D Cartesian grid for position and GaussLegendre angular grid for orientations, to obtain, at the minimum, the absolute solvation freeenergy of the solute and the equilibrium solvent density profile around it.
In comparison with direct MD simulation results, the DFT provides accurate representations of both microscopic structure and thermodynamic properties for a wide variety of solutes dissolved in molecular solvents including acetonitrile, water etc.. Unlike molecular simulations, DFT provides direct information on the free energy from which all thermodynamic properties can be derived.

12/03/09
Deanna Haunsperger  Carleton College
Bright Lights on the Horizon
AbstractWhat do a squarewheeled bicycle, a 17thcentury French painting, and the Indiana legislature all have in common? They appear among the many bright stars on the mathematical horizon, or perhaps, more correctly in the Math[ematical] Horizons. Math Horizons, the undergraduate magazine started by the MAA in 1994, publishes articles to introduce students to the world of mathematics outside the classroom. Some of mathematics’ best expositors have written for MH over the years; here are some of the highlights from the first ten years of Horizons.

12/04/09

12/04/09
Nolan Wallach  UCSD
QuaternionKaehler manifolds

12/07/09
Rosanna Haut  UCSD
Smoothing Penalized Splines

12/07/09
Louis Rowen  BarIlan University, Ramat Gan, Israel
Tropical Linear Algebra

12/08/09
Hans Wenzl  UCSD
Quantum groups and categorification  III

12/09/09
Mikael Passare  Stockholm University
Coamoebas and Mellin transforms
AbstractThe coamoeba of a complex polynomial $f$ is defined to be the
image of the hypersurface defined by $f$ under the mapping $\text{Arg}$
that
sends each coordinate $z_k$ to its argument $\arg z_k$. We shall discuss the
connection between coamoebas and the multidimensional Mellin transforms
of rational functions. 
12/10/09
Jacob Sterbenz  UCSD
Decay Estimates for Perturbations
AbstractIn this talk we'll focus on various dispersive estimates for the wave equation on Minkowski Space with a potential.

12/10/09
Louis Rowen  BarIlan University, Ramat Gan, Israel
Some Small Division Algebra Questions