Jan

01/05/15
V. Futorny  University of Sao Paulo
Classification of simple HarishChandra modules over Witt algebras
AbstractWe will discuss a classification of all simple weight modules over Witt algebras with finite multiplicities. The result generalizes a well known result of O. Mathieu for the Virasoro algebra. This is a joint result with Y. Billig (Carleton, Canada).

01/05/15
Ovidiu Munteanu  University of Connecticut
The geometry of Ricci solitons
AbstractI will present recent development about the structure of four dimensional shrinking Ricci solitons. I will show how some basic information about scalar curvature allows us to better understand such solitons. For example, assuming the scalar curvature is bounded, these manifolds must have their curvature operator nonnengative at
infinity. Furthermore, if the scalar curvature converges to zero, then they are asymptotically conical. Some generalizations in higher dimension will also be discussed. This talk is based on joint work with Jiaping Wang. 
01/06/15
Yao Yao  University of Wisconsin, Madison
Singularity and mixing in incompressible fluid equations
AbstractThe question of global regularity vs. finite time blowup remains open for many fluid equations. Even in the cases where global regularity is known, solutions may develop small scales as time progresses. In this talk, I will first discuss an active scalar equation which is an interpolation between the 2D Euler equation and the surface quasigeostrophic equation. We study the patch dynamics for this equation in the halfplane, and prove that the solutions can develop a finitetime singularity. I will also discuss a passive transport equation whose solutions are known to have global regularity, and our goal is to study how well a given initial density can be mixed if the incompressible flow satisfies some physically relevant quantitative constraints. This talk is based on joint works with A. Kiselev, L. Ryzhik and A. Zlatos.

01/08/15
Mamikon Ginovyan  Boston University
Efficient Nonparametric Estimation of Spectral Functionals for Continuoustime Gaussian Stationary Models.
AbstractThe problem of asymptotically efficient estimation of different kind of functionals for various statistical models has been extensively discussed in the literature. This talk is concerned with the estimation of spectral functionals for continuoustime Gaussian stationary models.
Suppose we observe a finite realization $\{X(t), \, 0\le t\le T\}$ of a centered realvalued stationary Gaussian process $\{X(t), \, t\in\mathbb{R}\}$ with an {\it unknown\/} spectral density $\theta(\lambda).$ Assume that $\theta(\lambda)$ belongs to a given (infinitedimensional) class ${\mbox{\boldmath$\Theta$}}$ of spectral densities possessing some smoothness properties. Let $\Phi(\cdot)$ be some {\it known\/} functional, the domain of definition of which contains ${\mbox{\boldmath$\Theta$}}$. The problem is to estimate the value
$\Phi (\theta)$ of the functional $\Phi(\cdot)$ at an unknown point
$\theta \in {\mbox{\boldmath$\Theta$}}$, and investigate the asymptotic properties of the suggested estimators, depending on the dependence structure of the model and smoothness structure of the "parametric" set ${\mbox{\boldmath$\Theta$}}$. The main objective is construction of asymptotically efficient estimators for $\Phi(\theta).$We define the concepts of $H$ and IKefficiency of estimators, based on the variants of H\'ajek convolution theorem and H\'ajekLe Cam local asymptotic minimax theorem, respectively, and show that the simple "plugin" statistic
$\Phi (I_T)$, where $I_T=I_T(\lambda)$ is the periodogram of the underlying process $X(t)$, is $H$ and IKasymptotically efficient estimator for a linear functional $\Phi (\theta),$ while for a nonlinear smooth functional $\Phi (\theta)$,
an $H$ and IKasymptotically efficient estimator is the statistic
$\Phi (\widehat \theta_T)$, where $\widehat \theta_T$ is a suitable sequence of the socalled "undersmoothed" kernel estimators of the unknown spectral density $\theta(\lambda).$Exact asymptotic bounds for minimax mean square risks of estimators of linear functionals will also be presented.

01/08/15
Elisa Lorenzo Garcia
Bad reduction of genus 3 curves with complex multiplication
AbstractLet C be a smooth, absolutely irreducible genus3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CMfield K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.
Joint work with Bouw, Cooley, Lauter, Manes, Newton, Ozman.

01/08/15
Choongbum Lee  MIT
Grid Ramsey problem and related questions
AbstractThe HalesJewett theorem is one of the pillars of Ramsey theory, from which many other results follow.
A celebrated result of Shelah from 1988 gives a significantly improved bound for this theorem. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. Hoping to further improve Shelah's result, more than twenty years ago, Graham, Rothschild and Spencer asked whether there exists a polynoimal bound for this lemma. In this talk, we present the answer to their question and discuss numerous connections of the cube lemma with other problems in Ramsey theory.
Joint work with David Conlon (Oxford), Jacob Fox (MIT), and Benny Sudakov (ETH Zurich)

01/08/15
Nikos Kapouleas  Brown University
Gluing constructions in Differential Geometry
AbstractI will discuss various geometric gluing constructions. First I will discuss constructions for Constant Mean Curvature hypersurfaces in Euclidean spaces including my earlier work for twosurfaces in threespace which settled the Hopf conjecture for surfaces of genus two and higher, and recent generalizations in
collaboration with Christine Breiner in all dimensions. I will then briefly mention gluing constructions in collaboration with Mark Haskins for special Lagrangian cones in $C^n$. A large part of my talk will concentrate on doubling and
desingularization constructions for minimal surfaces and on applications on closed minimal surfaces in the round spheres, free boundary minimal surfaces in the unit ball, and selfshrinkers for the Mean Curvature flow. Finally I will discuss my collaboration with Simon Brendle on constructions for Einstein metrics on fourmanifolds and related geometric objects. 
01/13/15
Xiaodong Li  University of Pennsylvania
Lowrank recovery: from convex to nonconvex methods
AbstractLowrank structures are common in modern data analysis and signal processing, and they usually play essential roles in various estimation and detection problems. It is challenging to recover the underlying lowrank structures reliably from corrupted or undersampled measurements. In this talk, we will introduce convex and nonconvex optimization methods for lowrank recovery by two examples. The first example is community detection in network data analysis. In the literature, it has been formulated as a lowrank recovery problem, and then SDP relaxation methods can be naturally applied. However, the statistical advantages of convex optimization approaches over other competitive methods, such as spectral clustering, were not clear. We show in this talk that the methodology of SDP is robust against arbitrary outlier nodes with strong theoretical guarantees, while standard spectral clustering may fail due to a small fraction of outliers. We also demonstrate that a degreecorrected version of SDP works well for a realworld network dataset with a heterogeneous distribution of degrees. Although SDP methods are provably effective and robust, the computational complexity is usually high and there is an issue of storage. For the problem of phase retrieval, which has various applications and can be formulated as a lowrank matrix recovery problem, we introduce an iterative algorithm induced by nonconvex optimization. We prove that our method converges reliably to the original signal. It requires far less storage and has much higher rate of convergence compared to convex methods.

01/14/15
Dustin Mixon  Air Force Institute of Technology
Phase retrieval: Approaching the theoretical limits in practice
AbstractIn many areas of imaging science, it is difficult to determine the phase of linear measurements. For example, in some applications, one only has access to the pointwise absolute value of various masked Fourier transforms of the desired signal. In this setting, the goal is to reconstruct the signal from the intensity measurements, that is, perform phase retrieval. This talk describes how to leverage ideas from spectral graph theory to design Fourier masks in a way that allows for efficient signal reconstruction.

01/15/15
Cristian Popescu  UCSD
The arithmetic of special values of Lfunctions
AbstractThe wellknown analytic class number formula, linking the special value at s=0 of the Dedekind zeta function of a number field to its class number and regulator, has been the foundation and prototype for the highly conjectural theory of special values of Lfunctions for close to two centuries. We will discuss generalizations of the class
number formula to the context of equivariant Artin Lfunctions which capture refinements of the BrumerStark and CoatesSinnott conjectures. These generalizations relate various algebraicgeometric invariants associated to a global field, e.g. its Quillen Kgroups and etale cohomology groups, to various special values of its Galoisequivariant Lfunctions. They illustrate the subtle interactions of number theory with complex and padic analysis, algebraic geometry, topology and homological algebra. 
01/15/15
Djordjo Milovic  Leiden University
Divisibility by 16 of class numbers in certain families of quadratic number fields
AbstractThe density of primes $p\equiv 1\pmod{8}$ (resp. $p\equiv
7\pmod{8}$) such that the class number of $\mathbb{Q}(\sqrt{p})$ (resp.
$\mathbb{Q}(\sqrt{2p})$) is divisible by $2^{k+2}$ is conjectured to be
$2^{k}$ for all positive integers $k$. The conjecture has been resolved
for $k = 1$ by the Chebotarev Density Theorem. For the family of quadratic
fields $\mathbb{Q}(\sqrt{2p})$, we use methods of Friedlander and Iwaniec
to prove the conjecture for $k = 2$. Moreover, we show that there are
infinitely many primes $p$ for which the class number of
$\mathbb{Q}(\sqrt{p})$ is divisible by $16$. 
01/15/15
Jeremy Marzuola  University of North Carolina
The relaxation of a general family of broken bond crystal surface models
AbstractWith Jon Weare (Chicago), we study the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solidonsolid and discrete Gaussian models. With computational experiments and theoretical arguments we are able to derive several partial differential equation limits identified (or nearly identified) in previous studies and to clarify the correct choice of surface tension appearing in the PDE and the correct scaling regime giving rise to each PDE. We also provide preliminary computational and analytic investigations of a number of interesting qualitative features of the large scale behavior of the models. The PDE models involved are fully nonlinear Fourth order diffusion type equations with many interesting geometric features. We will also discuss recent progress analyzing existence and regularity properties of solutions to such PDE.

01/20/15
Hao Ge  Beijing International Center for Mathematical Research, Peking University
Stochastic Processes at SingleMolecule and SingleCell Levels
AbstractDue to the advance of singlemolecule techniques, stochastic phenomena in chemistry and biology have been widely observed, which promotes the rapid development of stochastic modeling. I will discuss several stochastic processes in singlemolecule enzyme kinetics, transcriptional burst and toggle switch. The stochastic modeling not only can explain some unexpected law from the trajectory perspective, but also can help uncover certain molecular mechanism and carefully analyze the effect of noise within gene regulation.

01/22/15
Miklos Racz  UC Berkeley
From trees to seeds: on the inference of the seed from large random trees
AbstractI will discuss the influence of the seed in models of randomly growing trees; in particular, I will focus on the preferential attachment and uniform attachment models. In both of these models, different seeds lead to different distributions of limiting trees from a total variation point of view. I will discuss the differences and similarities in proving this for the two models. This is based on joint work with Sebastien Bubeck, Ronen Eldan, and Elchanan Mossel.

01/22/15
Alireza Salehi Golsefidy  UCSD
Finitely generated linear groups and their applications in number theory, combinatorics, topology, etc.
AbstractI will explain part of my journey in this beautiful subject:
* Superstrong approximation and its applications to other areas of math.
* Counting lattices.
* Ratner's theorems and its applications to number theory.
In each one of these topics, some open problems will be mentioned.
(Disclaimer: Most likely one of these topics will be discussed only briefly because of time restriction.)

01/22/15
Peter Stevenhagen  Universiteit Leiden
Universality of adelic groups
AbstractAngelakis proved in his thesis (2015) that there are many different imaginary quadratic fields that all have the "same" absolute abelian Galois group, i.e., their absolute abelian Galois group is isomorphic to some universal profinite group.
In this talk, we show that his techniques can be used to prove similar results for the adelic point groups associated to elliptic curves.

01/27/15
Caroline Uhler  Institute of Science and Technology Austria
Gene Regulation in Space and Time

01/29/15
Todd Kemp  UCSD
Beyond universality in random matrix theory
AbstractIn random matrix theory, we study the histogram of eigenvalues of matrices sampled from given distributions on their entries, asymptotically as the dimension grows. The (computationally) nicest case  independent Gaussian entries  was initiated by Wigner in the 1950s, and by the 1980s this case was pretty completely understood.
In the last decade, the subject has exploded. Most attention has thus far been focused on two natural broad generalizations of the Gaussian case: either to matrices with independent entries sampled from some other distribution, or matrices whose joint density of entries has a logconcave potential. In both scenarios, we now know the asymptotic behavior is "universal": the limit law of eigenvalues, their fluctuations around this limit, and finer statistics like asymptotic spacing and edge behavior, are all the same essentially independent of the specific model used.
In this talk I will discuss the main story of random matrices as we know it today, and also discuss a very new direction: a third broad generalization of "Gaussian" matrices. Thinking of a Gaussian as the solution to the heat equation on a linear space of matrices, I have been studying the eigenvalues of heat kernel distributed random matrices on Lie groups. As we will discuss, some of the "universal" behavior from the studied models persists (like the size and form of the fluctuations), but in most cases, these models yield completely new asymptotics that we are only beginning to understand.

01/29/15
Melvin Leok  UCSD
General Methods for Constructing Variational Integrators

01/29/15
Grzegorz Banaszak  Adam Mickiewicz University and UCSD
Divisibility in Kgroups and classical conjectures in Number Theory
AbstractI will discuss divisibility and wild kernels in algebraic Ktheory of number fields $F$ and present basic results concerning the divisible elements in Kgroups. Without appealing to the QuillenLichtenbaum conjecture one can prove that the group of divisible elements is isomorphic to the corresponding group of \' etale divisible elements.
One can apply this result for the proof of the $lim^1$ analogue of the QuillenLichtenbaum conjecture. One can also apply it to investigate: the imbedding obstructions in homology of $GL,$ the splitting obstructions for the Quillen localization sequence, the order of the group of divisible elements via special values of $\zeta_{F}(s).$ I will discuss the relation of divisible elements with KummerVandiver and Iwasawa conjectures.
I will also present recent results, joint with Cristian Popescu, concerning BrummerStark conjecture and Galois equivariant Stickelberger splitting map in Quillen localization sequence. The Stickelberger splitting map is a basic tool to investigate the structure of the group of divisible elements.

01/30/15
David Meyer  UCSD
Nonlinear Schrodinger equations and computation
Feb

02/02/15
Xingting Wang  UCSD
Universal enveloping algebras of Poisson algebras
AbstractThe notion of universal enveloping algebra is introduced concerning a commutative Poisson algebra in order to study the category of Poisson modules over the Poisson algebra. The main purpose of this talk is to propose the study of universal enveloping algebra for its own sake. Some basic ringtheoretic and homological properties of the universal enveloping algebra are proved. We also ask some open questions, which suggests us to use universal enveloping algebra to understand the Poisson structure of any commutative algebra.

02/03/15
Deanna Needell  Claremont McKenna College
Practical compressive sampling with frames
AbstractCompressed sensing is a new field that arose as a response to inefficient traditional signal acquisition schemes. Under the assumption that the signal of interest is sparse, one wishes to take a small number of linear samples and later utilize a reconstruction algorithm to accurately recover the compressed signal. Typically, one assumes the signal is sparse itself or with respect to some fixed orthonormal basis. However, in applications one instead more often encounters signals sparse with respect to a tight frame which may be far from orthonormal. In the first part of this lecture, we will introduce the compressed sensing problem as well as recent results extending the theory to the case of sparsity in tight frames. The second part of the lecture focuses on dictionary learning which is also a new field, but closely related to compressive sensing. Briefly speaking, a dictionary is an overcomplete and redundant system consisting of prototype signals that are used to express other signals. Due to the redundancy, for any given signal, there are many ways to represent it, but normally the sparsest representation is preferred for simplicity and easy interpretability. A good analog is the English language where the dictionary is the collection of all words (prototype signals) and sentences (signals) are short and concise combinations of words. In this lecture, we will introduce the problem of dictionary learning, its origin and applications, and existing solutions.

02/03/15
Marta Farre  ICMAT, Spain
Constrained Mechanics and the Inverse Problem

02/05/15
Jiawang Nie  UCSD
From local optimization to global optimization, and from matrix to tensor
AbstractThis talk gives an introduction to the most recent advances in optimization and numerical linear algebra.
In classical optimization theory, much has been known about local optimizers. There are standard conditions for local optimality, like the KarushKuhnTucker (KKT) condition, second order sufficiency condition (SOSC), strict complementarity condition (SCC). There are no such conditions for global optimality in nonlinear programming theory. However, when all the functions are polynomial, there is a global optimality condition, which are closely related to KKT, SOSC and SCC.
In numerical linear algebra, much has been known about matrix computations, like ranks, eigenvalues, singular value decompositions, low rank approximations and matrix completions. Tensors are natural generalizations of matrices, arising from wide applications. Similar questions like for matrices need to be solved for tensors. However, such questions are mostly open for tensors.
This talk will give an overview of the new research results in the area, as well as the remaining challenges.

02/05/15
Melvin Leok  UCSD
Multisymplectic Discretizations of Field Theories

02/05/15
Danny Neftin  University of Michigan
The Sylow subgroups of the absolute Galois group of Q.
AbstractFollowing a question of Serre, the Sylow subgroups of the absolute Galois group of a padic field were studied and completely understood by Labute. However, the structure of the pSylow subgroups of the absolute Galois group of the field of rational numbers is much more subtle and mysterious. We make progress towards its determination via a surprisingly simple decomposition. Joint work with Lior BarySoroker and Moshe Jarden.

02/05/15
Danny Neftin  University of Michigan
Galois groups of rational functions
AbstractA fundamental invariant associated to every complex rational function f is its monodromy group, that is, the Galois group of the covering $f:P^1>P^1$ on the projective line $P^1$. We shall discuss the accumulating work towards determining the degree n complex rational functions with a specified monodromy group that is not $A_n$ or $S_n$, and its applications to problems in number theory, complex analysis, and complex dynamics. Joint work with Michael Zieve.

02/06/15
Frank Bauerle and Anthony Tromba  UC Santa Cruz
UC Calculus Online
AbstractWe will describe UC's Calculus Online, now available to all UC students through our new cross campus enrollment system as well as to all non matriculated students including foreign nationals. Calculus I for Science and Engineering Students has been successfully running for over a year and Calculus II since last Spring. Calculus III and IV are currently in development.
The courses have many components, from introductory welcome lectures, historical enrichment video lectures, online lecture videos (all synchronized with an online interactive etext originally developed for print by UCLA Professor Jon Rogawski), to an online discussion forum platform all accessible via UC's Canvas Learning Management System. We would very much welcome questions and suggestions.

02/09/15
Shaunak Das  UCSD
Vector Bundles on Perfectoid Spaces
AbstractPerfectoid spaces were very recently introduced by Scholze and KedlayaLiu, independently. These objects provide geometric context to the fieldofnorms isomorphism from padic Hodge Theory, which relates absolute Galois groups in characteristic 0 and characteristic p. In this talk, I will discuss what perfectoid spaces are, why they are soo hawt right now, and then present some natural questions about their geometry which I am interested in answering.

02/09/15
Louis Rowen  BarIlan University
Subspaces of division algebras
AbstractMuch of the structure of a division algebra can be garnered from the structure of its subspaces. For example, a division algebra of prime degree is cyclic if and only if it has a subspace each of whose elements have $p$power in the center. We consider this and other conditions on the subspace, and describe the growth of $\{ \dim_K (KaK)^i : i \geq 1 \}$, for a maximal separable subfield $K$ of a central simple algebra $A$ and $a \in A \setminus K.$ We tie this to Brauer factor sets, the trace form, and the commutator question. This is joint work with Matzri, Saltman, and Vishne, and in part with Chapman.

02/10/15
Holger Dullin  University of Sydney
Topology of integrable Hamiltonian systems

02/11/15
Ivan Shestakov  University of Sao Paulo, Brazil
The Freiheitssatz for generic Poisson algebras.
AbstractA generic Poisson algebra is a commutative associative algebra with an
anticommutative product (a bracket), which satisfies the Leibnitz identity but, in general, does not satisfy the Jacobi identity. We prove that the Freiheitssatz holds in the variety of generic Poisson algebras. In other words, every nontrivial equation over the free generic Poisson algebra P has a solution in some extension of P. Earlier this result was proved for ordinary Poisson algebras by L.Makar Limanov and U.Umirbaev. This is a joint work with P.Kolesnikov and L.Makar Limanov. 
02/11/15
Veniamin Morgenshtern  Stanford University
Stable SuperResolution of Positive Sources
AbstractThe resolution of all microscopes is limited by diffraction. The observed signal is a convolution of the emitted signal with a lowpass kernel, the pointspread function (PSF) of the microscope. The frequency cutoff of the PSF is inversely proportional to the wavelength of light. Hence, the features of the object that are smaller than the wavelength of light are difficult to observe. In singlemolecule microscopy the emitted signal is a collection of point sources, produced by blinking molecules. The goal is to recover the location of these sources with precision that is much higher than the wavelength of light. This leads to the problem of superresolution of positive sources in the presence of noise. We show that the problem can be solved using convex optimization in a stable fashion. The stability of reconstruction depends on Rayleighregularity of the support of the signal, i.e., on how many point sources can occur within an interval of one wavelength. The stability estimate is complemented by a converse result: the performance of the convex algorithm is nearly optimal. I will also give a brief summary on the ongoing project, developed in collaboration with the group of Prof. W.E. Moerner, where we use the theoretical ideas to improve microscopes.

02/12/15
Takashi Kumagai  Kyoto University
Heat kernel estimates and local CLT for random walk among random conductances with a powerlaw tail near zero
AbstractWe study ondiagonal heat kernel estimates and exit time estimates for continuous time random walks (CTRWs) among i.i.d. random conductances with a powerlaw tail near zero. For two types of natural CTRWs, we give optimal exponents of the tail such that the behaviors are standard (i.e. similar to the random walk on the Euclidean space) above the exponents. We then establish the local CLT for the CTRWs. We will also compare our results to the recent results by AndresDeuschelSlowik.
This talk is a joint work with O. Boukhadra (Constantine) and P. Mathieu (Marseille). 
02/12/15
Robert Won  UCSD
SET and AG(4,3)
AbstractThe card game SET is a game of pattern recognition. In this talk, we discuss the interesting mathematics behind a deck of SET cards. We will discuss how SET can be used to visualize the finite affine geometries of order 3. We also present recent results and discuss what Terence Tao has described as "perhaps [his] favourite open question."
This talk should be accessible to undergraduates and graduate students of all ages. The only background required is algebra on the level of Math 100 and combinatorics on the level of an algebraist.
(Joint work with M. Follett, K. Kalail, E. McMahon, and C. Pelland.)

02/12/15
Rayan Saab  UCSD
A sampling of mathematical signal processing
AbstractMathematical signal processing (aka applied and computational harmonic analysis) deals with the theory of data acquisition, representation, reconstruction (and more). Viewing a signal as a vector in an appropriate space, one seeks sampling theorems that prescribe how to measure the signal, and subsequently recover it from the measurements. A classical example is the standard sampling theorem for bandlimited functions. On the other hand, compressing (transform coding) a class of signals entails representing its members sparsely in an appropriate system. So one is interested both in finding such a system and obtaining theoretical guarantees on the error resulting from representing functions using a few its elements. Also of interest are practical methods of digitizing the measurements, and here we seek theoretical guarantees to quantify tradeoffs between the number of measurements and bits, and the reconstruction accuracy.
In recent years, this area has seen many exciting developments based on the following simple observation. Many realworld signals can be modeled as vectors having only a few degrees of freedom, and more specifically as linear combinations of relatively few basis elements. Such vectors are said to be sparse. Great strides in sparse approximation theory and its application have been made, spurred by the rapidly growing area of compressed sensing. This is a sampling paradigm that entails efficiently recovering estimates of sparse Ndimensional vectors from m linear measurements where $m<<N$.
We will provide an introduction to some of the essentials of compressed sensing, discuss its extensions, draw connections to some of the areas of mathematics and computer science that it interacts strongly with, and give an overview of some interesting research problems.

02/12/15
Anthony Bloch  University of Michigan
Mechanics and Optimal Control

02/12/15
Burkhard Wilking  UC Berkeley
Some new curvature identities and applications to Ricci flow invariant curvature conditions

02/12/15
Anthony Bloch  University of Michigan
On the geometry of integrable Hamiltonian and dissipative flows

02/13/15
Federico Buonerba  Courant Institute of Mathematical Sciences
Resolution of tame quotient singularities
AbstractThere is still no analogue of Hironaka's type resolution for algebraic varieties over fields of positive characteristics. However a theorem of DeJong states that, up to taking a purely inseparable cover, there exists a birational model whose singularities are at worst quotient. In this talk I will discuss a resolution algorithm of tame quotient singularities.

02/18/15
Jason Bell  University of Waterloo
Applications of padic analysis to algebra and geometry
AbstractWe consider some recent applications of techniques of padic analysis to algebra and geometry. Specifically, we consider three applications. First, we show that it gives a solution to a problem of Keeler, Rogalski, and Stafford asking to show that if the orbit of a point under an automorphism of a complex projective variety has the property that it intersects some subvariety infinitely often then the orbit cannot be Zariski dense. Next, we show that one can give a new proof of a result of Bass and Lubotzky showing that the Burnside problem has an affirmative solution for automorphism groups of quasiprojective varieties. Finally, we consider an application that gives a result of Bogomolov and Tschinkel: a K3 surface defined over a number field $F$ with an infinite automorphism group has a dense set of $K$points for some finite extension of $F$. This includes joint work with Dragos Ghioca, Zinovy Reichstein, Daniel Rogalski, Sue Sierra, and Tom Tucker.

02/19/15
James McKernan  UCSD
How many symmetries can a polynomial have?
AbstractIn this talk we explain how this question has many different types of answers, depending on what you mean by "many" and what you mean by "symmetry". We also explore how answering this question leads from very classical algebraic geometry to the modern theory of classification of varieties.

02/19/15
Wotao Yin  UCLA
Operator Splitting and Optimization
AbstractOperator splitting schemes break a complicated and possible nonsmooth optimization problem into simple matrixvector multiplication, gradient, projection, and proximal steps. The resulting algorithms are often short, easy to code, and have (nearly) stateoftheart performance for largescale optimization problems that arise in machine learning, compressed sensing, medical imaging, geophysics, and bioengineering. The importance of operator splitting, a technique that dates back to the 1950’ and since then been widely used in numerical linear algebra and numerical PDE, has significantly increased in the past decade.
This talk will review the basic operator splitting schemes and introduce a new splitting scheme. Their special cases cover a large number of existing algorithms such as von Neumann's alternating projection, iterative softthresholding algorithm, ADMM, and various primaldual algorithms. Their convergence results are presented. Through examples, we also demonstrate that they lead to highperformance lowcost methods for largescale optimization problems.
This talk includes joint work with Damek Davis, Wei Deng, Mingjun Lai, Zhimin Peng, and Ming Yan.

02/19/15
Padmini Rangamani  Department of Mechanical and Aerospace Engineering, UCSD
Viscoelastic Lipid Bilayers: Theory and Applications
AbstractThe theory of intrasurface viscous flow on lipid bilayers is developed by combining the equations for flow on a curved surface with those that describe the elastic resistance of the bilayer to flexure. The model is derived directly from balance laws and augments an alternative formulation based on a variational principle. Conditions holding along an edge of the membrane are emphasized and the coupling between flow and membrane shape is simulated numerically. Particular applications that will be discussed in this talk include lipid flow on minimal surfaces, osmotic pressure drive membrane deformation, and flow due to protein adsorption.

02/19/15
Yuan Yao  Peking University
Geometric and Topological Methods for Data Analysis
AbstractVoting has been an important topic for human activities and a central theme in the social choice theory in Economics, which is featured with the celebrated Impossibility Theorems by Nobel Laureates Ken Arrow and Amartya Sen. Despite of the intrinsic conflicts between the faithful representation of individuals and the desire for consistent social orders, in reality we are still looking for possible preference aggregation rules out of impossibilities. Hodge Theory, as a bridge between the algebraic topology and geometry, is surprisingly enabling us a tool of preference aggregation as a generalization of the classical Borda count, arguably the most consistent and tractable social choice rule. It not only enables us to find aggregated preference with nearly linear complexity algorithms to deal with the rapid growth of crowdsourcing data, but also provides us ways to characterize the conflicts of interests arising locally or globally. We shall discuss these from a revisit of those impossibility theorems to see what is possible that Hodge decomposition provides us.

02/20/15
Michael Kasa  UCSD
Log geometry and relative GromovWitten invariants
AbstractRelative GromovWitten theory gives virtual counts of curves with specified tangency conditions. The most natural setting for this theory is in the category of log schemes. In this talk, I will describe the basics of log geometry, discuss their relationship with relative GromovWitten theory, and provide a concrete sample calculation.

02/24/15
Jorge Cortes  UCSD, Mechanical and Aerospace Engineering
Distributed Control Theory I

02/24/15
Sonia Martinez  UCSD, Mechanical and Aerospace Engineering
Distributed Control Theory II

02/24/15
Kaave Hosseini  UCSD
An Improved lower bound for arithmetic regularity
AbstractThe arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemeredi regularity lemma in graph theory. It shows that for any abelian group G and any bounded function $f : G \rightarrow [0, 1]$, there exists a subgroup $H \leq G$ of bounded index such that, when restricted to most cosets of $H$, the function f is pseudorandom in the sense that all its nontrivial Fourier coefficients are small. Quantitatively, if one wishes to obtain that for $1  \epsilon$ fraction of the cosets, the nontrivial Fourier coefficients are bounded by $\epsilon$, then Green shows that $G/H$ is bounded by a tower of twos of height $1/\epsilon^3$. He also gives an example showing that a tower of height $\Omega(\log 1/\epsilon)$ is necessary. Here, we give an improved example, showing that a tower of height $\Omega(1/\epsilon)$ is necessary.
Joint work with Shachar Lovett, Guy Moshkovitz, and Asaf Shapira.

02/25/15
Penny Haxell  University of Waterloo
Morphing planar graphs
AbstractConsider two straightline planar drawings G and H of the same planar triangulation, in which the outer face is fixed. A morph between G and H is a continuous family of drawings of the triangulation, beginning with G and ending with H. We say a morph between G and H is planar if each intermediate drawing is a straightline planar drawing of the triangulation. A morph is called linear if each vertex moves from its initial position in G to its final position in H along a line segment at constant speed. It is easy to see that in general the linear morph from G to H will not be planar.
Here we consider the algorithmic problem of finding a planar morph between two given drawings G and H with fixed outer face. For various reasons it is desirable to find morphs in which each vertex trajectory is fairly simple. Thus we focus on the problem of constructing a planar morph consisting of a polynomial number of steps, in which each step is a planar linear morph.
(Joint work with Fidel BarreraCruz and Anna Lubiw)

02/26/15
Yu Gu  Stanford University
A twoscale expansion for equations with random coefficients: a probabilistic approach
AbstractRecently, quantitative stochastic homogenization of operators in divergence form has witnessed important progress, starting from the work of Gloria and Otto. Our goal is to go beyond the error bound and further analyze the statistical fluctuations around the homogenized limit. Using a probabilistic representation, the KipnisVaradhan method applied to diffusion in random environment, and a quantitative martingale central limit theorem, we prove a pointwise twoscale expansion by a stationary corrector. This is joint work with JeanChristophe Mourrat.

02/26/15
Bennett Chow  UCSD
Ricci Shrinkers
AbstractRicci shrinkers are shrinking selfsimilar solutions to the Ricci flow. These objects arise as limits in the study of singular solutions of the Ricci flow. We highlight some results on the geometry of Ricci shrinkers.

02/26/15
Debra Lewis  UC Santa Cruz
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry

02/26/15
Joseph Palmer  UCSD
The moduli space of semitoric integrable systems

02/26/15
Hans G. Othmer  School of Mathematics & Digital Technology Center, University of Minnesota
From Crawlers to Swimmers  Mathematical and Computational Problems in Cell Motility
AbstractCell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the detection and transduction of extracellular chemical and mechanical signals, integration of the signals into an intracellular signal, and the spatiotemporal control of the intracellular biochemical and mechanical responses that lead to force generation, morphological changes and directed movement. We will discuss some of the mathematical and computational challenges that the integration of these processes poses and describe recent progress on some component processes.
Mar

03/03/15
Joe Salamon  UCSD, Physics
Variational Discretizations of Classical Gauge Field Theories

03/05/15
Mark Kempton  UCSD
Nonbacktracking random walks on graphs
AbstractRandom walks on graphs are wellstudied, and numerous results exist relating properties of a random walk on a graph to the spectra of various matrices associated with the graph. Particularly, the eigenvalues of the adjacency matrix of a graph give us information about the rate of convergence of a random walk to its stationary distribution. Less wellunderstood are nonbacktracking random walks, which are random walks with the extra condition that we cannot return to the immediately previous state. These are much harder to analyze in general. A paper of Alon, Benjamini, Lubetzky, and Sodin from 2007 proves that for regular graphs, in most cases a nonbacktracking random walk will converge to its stationary distribution more quickly than an ordinary random walk. We will discuss some known results on random walks ways to approach the generalization of these results to nonbacktracking random walks.

03/05/15
Brendon Rhoades  UCSD
Progress and problems in cyclic sieving
AbstractThe cyclic sieving phenomenon is a decadeold object in enumerative combinatorics introduced by Reiner, Stanton, and White related to counting the fixedpoint set sizes associated with a finite cyclic group acting on a finite set. We will give examples of the CSP for combinatorial actions on Young tableaux, polygon dissections, and set partitions. We will see that, while the statement of the CSP is purely enumerative, the ``best" proofs of CSPs are algebraic and instances of the CSP can predict results in algebra and geometry.

03/05/15
Vladimir Baranovsky  UC Irvine
Quantization of line bundles
AbstractLet X be an algebraic symplectic variety, and assume that its structure sheaf admits a deformation quantization. A line bundle on a Lagrangian subvariety of X may be viewed as a module over the structure sheaf of X and we could ask weather the module structure admits a deformation quantization as well. We discuss some old and new results in this direction.

03/05/15
Zhaojun Bai  UC Davis
Variational principles and Computation of Linear Response Eigenvalue Problems
AbstractLinear response eigenvalue problems (LREPs) arise from the study of collective motion of many particle systems, such as excited states of electronic structures. Large scale LREPs are challenging due to its nonsymmetric structure. In this talk,
we will present recent theoretical results on variational principles of LREPs and discuss conjugate gradientlike algorithms. Numerical results of very large LREPs for computing multiple lowlying excitation energies of molecules by the timedependent density functional theory will be presented. This is a joint work with Rencang Li, Dario Rocca and Giulia Galli. 
03/09/15
Don Passman  University of Wisconsin
Traces of Algebraic Elements in Group Algebras
AbstractIf $K[G]$ denotes the group algebra of G over the field K, then the trace map $tr : K[G] \to K$ picks off the identity coefficient of each element of the ring. In this talk, I will discuss what is known about traces of algebraic elements of $K[G]$. Of particular interest are the traces of idempotents and nilpotent elements. If time permits, I will also consider analogous results for twisted group algebras.

03/10/15
Fox Cheng  UCSD
Analysis and Numerical Treatment of Linearized Elastostatic Problem with Random Media
AbstractStochastic mechanical behaviors of random media is relevant to various of
engineering fields, One example of random media is, in order to simulate the fault formation of earthquake, stochastic treatment on ground surface is applied which consists of several layers of not fully known properties and structures.In this presentation, we examine a general linearized elastostatic problem in random media. a complete analysis in solution space is provided including existence and uniqueness. The single integral formulation of weak form and stochastic collocation method are applied to solve this problem. Moreover, the prior error estimators of stochastic collocation method are derived which imply the rate of convergence is exponential along with the order of polynomial increasing in the space of random
variables. As expected, the numerical experiments admit the exponential rate of convergence verified by a posterior error analysis. At last, a adaptive strategy derived by the posterior error analysis is designed. 
03/11/15
Corey D. Stone  UCSD
Higher Fitting ideals and special values of Lfunctions in Iwasawa theory

03/12/15
Mark Kempton, James Pascoe, Andy Wilson, David Zimmermann  UCSD
How to get a postdoc in mathematics
AbstractThis will be a panel discussion on the academic job search given by current 5th year graduate students. The panel will be interactive, so come prepared with questions!

03/12/15
Michael Holst  UCSD
A Brief Look at Some Mathematics Research Problems in General Relativity
AbstractThe Einstein constraints equations are of fundamental interest in the the study of Einstein's theory of general relativity. This coupled nonlinear elliptic system must also be solved reliably and efficiently for gravitational wave simulation. The equations have been studied intensively for half a century; they are a particular example of a "critical exponent" problem, often arising in geometric analysis.
In this lecture, we begin with an overview of the most useful mathematical formulation of the constraint equations, and then summarize the known existence, uniqueness, and multiplicity results through 2008. We then present a number of new existence and multiplicity results developed since 2008 that substantially extend the solution theory for the constraint equations. The techniques needed for developing new results are wideranging, and include fixedpoint arguments, maximum principles, a priori estimates, bifurcation theory, and other techniques in nonlinear analysis and partial differential equations.
We then shift gears a bit and consider Galerkin and PetrovGalerkin type
approximation methods for developing "good" numerical methods for solving this system. We examine how one proves rigorous error estimates for particular classes of numerical methods, including both classical finite element methods and newer methods from the finite element exterior calculus.This project is joint work with a number of collaborators over several years.

03/13/15
Yuri Bahturin  Memorial University of Newfoundland
Growth of subalgebras and subideals in free Lie algebras
AbstractThis is a joint work with Alexander Olshanskii. We study the exponents of the growth and cogrowth of subalgebras and subideals in free Lie algebras. In the case of ideals it is known that the growth of a nonzero ideal of a free Lie algebra is equivalent to the growth of the whole algebra. In the case of finitely generated subalgebras the same can be said about the cogrowth of proper finitely generated subalgebras. The most intriguing case is that of subideals.

03/13/15
Kimiko Yamada  Okayama University of Science
Singularities and Kodaira dimension of moduli of stable sheaves over elliptic surfaces
AbstractLet M be the moduli scheme of stable sheaves on a complex elliptic
surface. We want to know its birational structure, especially its Kodaira
dimension. To this end, it is important to understand its singularities.
What is known about such problems now? 
03/17/15
Fraydoun Rezakhanlou  UC Berkeley
PoincareBirkhoff stochastic fixed point theorems

03/18/15
Fraydoun Rezakhanlou  UC Berkeley
Generalized Smoluchowski Equations and Scalar Conservation Laws

03/18/15
Nolan Wallach  UCSD
Quantum nonlocality without entanglement
AbstractThis is joint work with Jiri Lebl and Asif Shakeel. We consider orthonormal bases in n qubits that consist of product states (unentangled orthonormal basisUOB) and a device for each qubit that can do an arbitrary unitary transformation and a measurement on the qubit. Given a UOB and an element in the basis an LOCC protocol for determining which element we have chosen involves the following steps:
1. Set up and order for doing the local operations (unitary operation and measurement) by the devices.
2. After each local operation in this order the outcome of all of the earlier operations is communicated to the next instrument in the order and that instrument chooses it's local operation using the outcomes of all the previous operations.
It has been shown that in 3 or more qubits there are UOB such that there is no protocol that can pick out a specific basis element with certainty. We show that in n qubits the generic UOB does not have this nonlocality and completely classify these UOB's. Thus the ones not on our list have this nonlocality.

03/18/15
(Kim) Thada Udomprapasup  UCSD
Diffusion Processes and Dirichlet Forms

03/18/15
Felix Lazebnik  University of Delaware
New results for some families of algebraically defined graphs
AbstractIn this talk we discuss some recent results on Wenger graphs and their modification, including spectra, expansion and cycles lengths. Most of these results represent joint work with S. Cioaba, W. Li, A. Thomason and Y. Wang.

03/19/15
Mona Merling  Johns Hopkins University
Equivariant algebraic Ktheory
AbstractThe algebraic K theory space $K(R)$ is defined as a topological group completion, which on $\pi_0$ is just the usual algebraic group completion of a monoid which yields $K_0(R)$. Amazingly, it turns out that this space not only has a multiplication on it which is associative and commutative up to
homotopy, but it is an infinite loop space. This means that it represents
a spectrum (the stable analogue of a space), and therefore a cohomology
theory. We construct equivariant algebraic Ktheory for Grings. However,
spectra with Gaction (called naive Gspectra) are not robust enough for
stable homotopy theory, and the objects of study in equivariant stable
homotopy theory are genuine Gspectra, which correspond to cohomology
theories graded on representations.Our construction of ``genuine" equivariant algebraic Ktheory recovers as
its fixed points the Ktheory of twisted group rings, and as particular
cases equivariant topological real and complex Ktheory, Atiyah's Real
Ktheory and statements previously formulated in terms of naive Gspectra
for Galois extensions. For example, we can reinterpret the map from the
QuillenLichtenbaum conjecture and the assembly map from Carlsson's
conjecture in terms of genuine Gspectra and their fixed points.We will not assume background in topology and will explain all the concepts from homotopy theory that arise in the talk.

03/19/15
Edward Witten  IAS
Knots and Quantum Theory

03/19/15
Nitu Kitchloo  Johns Hopkins University
Symmetries of Symplectic category and a conjecture of Kontsevich
AbstractMotivated by perturbative computations of Feynman integrals, Kontsevich has conjectured that a certain group known as the GrothendieckTeichmuller group acts on the moduli space of Field theories. Moreover he has explicitly described this action in certain examples. We first describe a stable context for this question, which can be interpreted as inverting free Bosonic field theories. We then show
that a quotient of the GT group acts on the stable object in agreement with computations made by Kontsevich. We will try to make this talk as self contained as possible. 
03/20/15
Gregory Pearlstein  Texas A&M
Boundary components of MumfordTate domains
AbstractBy the work of Griffiths, the cohomology of a family of complex projective manifolds determines a period map from the base of the family to the quotient of a flag domain D. In the case where D is hermitian symmetric, these quotients admit a number of partial compactifications including the BailyBorel and toroidal AMRT compactifications. I describe recent work with Matt Kerr on computing the MumfordTate group of the analogs of the ARMT boundary components of a degeneration of Hodge structure arbitrary weight.
Apr

04/02/15
Matt Junge  PhD Student, University of Washington
Splitting hairs (with choice)
AbstractIn the past decade computer science literature has studied the effect of introducing random choices to classical processes. For example, sequentially place n balls into n bins. For each ball, two bins are sampled uniformly and the ball is placed in the emptier of the two. This process does a much better job of evenly distributing the balls than the "choiceless" version where one places each ball uniformly.
Consider the continuous version: Form a random sequence in the unit interval by having the n*th* term be whichever of two uniformly placed points falls in the larger gap between the previous n1 points. I'll confirm the intuition that this sequence is a.s. equidistributed, solving an open problem from Itai Benjamini, Pascal Maillard and Elliot Paquette. The history goes back a century to Weyl and more recently to Kakutani. Several open problems will be discussed.

04/02/15
Jay Cummings  UCSD
Math and Juggling at UCSD
AbstractThe mathematics of juggling began with the task of characterizing all possible physical juggling patterns. Over the past few decades this study has expanded, inspiring related questions from many areas of math. In this talk we will discuss several new probabilistic, algebraic and combinatorial results and state some unsolved problems. Attendees are invited to bring chainsaws and/or lit torches for the interactive portion of the talk.
Light refreshments will be provided thanks to the sponsorship of the GSA.

04/02/15
Robin TuckerDrob  Rutgers University
Treeability and planarity in measured group theory
AbstractI will discuss recent joint work with Conley, Gaboriau, and Marks in which we show that all free pmp actions of groups with planar Cayley graphs are treeable. This provides the first examples of nonamenable groups with one end which are strongly treeable.

04/03/15
Ivan Cheltsov  University of Edinburgh
Cylinders in del Pezzo surfaces
AbstractFor a projective variety X and an ample divisor H on it, an Hpolar cylinder in X is an open ruled affine subset whose complement is a support of an effective Qdivisor Qrationally equivalent to H. This notion links together affine, birational and Kahler geometries. I will show how to prove existence and nonexistence of Hpolar cylinders in smooth and mildly singular del Pezzo surfaces (for different polarizations). The obstructions comes from log canonical thresholds and Fujita numbers. As an application, I will answer an old question of Zaidenberg and Flenner about additive group actions on the cubic Fermat affine threefold cone. This is a joint work with Jihun Park (POSTECH) and Joonyeong Won (KAIST).

04/07/15
Randolph Bank  UCSD
Some Recent Results for Adaptive Finite Elements
AbstractWe will discuss our ongoing investigation of adaptive strategies for finite element equations. We show first that under modest assumptions, any robust and efficient a posteriori error indicator must behave as simple interpolation error for the exact finite element solution. We then use interpolation error to study several popular h and hp adaptive algorithms.

04/07/15
Guoce Xin  Center for Combinatorics, Nankai University
The theory of Constant Term Identities with applications to Combinatorics.
AbstractThis will be the first in a series of talks on the theory of evaluating constant term identities and their applications to combinatorics and algebra.

04/09/15
Jason Schweinsberg  UCSD
Rigorous results for a population model with selection
AbstractWe consider a model of a population of fixed size $N$ in which each individual acquires beneficial mutations at rate $\mu$. Each individual dies at rate one, and when a death occurs, an individual is chosen with probability proportional to the individual's fitness to give birth. We obtain rigorous results for the rate at which mutations accumulate in the population, the distribution of the fitnesses of individuals in the population at a given time, and the genealogy of the population. Our results confirm predictions of Desai and Fisher (2007), Desai, Walczak, and Fisher (2013), and Neher and Hallatschek (2013).

04/09/15
Panel of speakers  UCSD
How to find an advisor in the math department
AbstractThis will be a panel discussion on the process of finding a thesis advisor. The panel will be interactive, so come prepared with questions!
Sponsored by the GSA.

04/09/15
Xinwen Zhu  California Institute of Technology
On some Tate cycles on Shimura varieties
AbstractI will first describe certain conjectural Tate classes in the middle dimensional etale cohomology of many Shimura varieties over finite fields (e.g. Hilbert and Picard modular surfaces at inert primes). According to the Tate conjecture, there should exist corresponding algebraic cycles. Surprisingly, we find that these cycles are provided by the supersingular (or more precisely basic) loci of these Shimura varieties. This is based on a joint work with Liang Xiao.

04/10/15
Brian Lehmann  Boston College
The geometric constants in Manin's Conjecture
AbstractManin's Conjecture predicts that the behavior of rational points on a variety X is controlled by certain geometric constants associated to X. I will discuss how the minimal model program can be used to analyze the behavior of these constants. This is joint work with Sho Tanimoto and Yuri Tschinkel.

04/13/15
Manny Reyes  Bowdoin College
Diagonalizable algebras of operators on infinitedimensional vector spaces
AbstractGiven a vector space $V$ over a field $K$, let $\mathrm{End}(V)$ denote the algebra of linear endomorphisms of $V$. If $V$ is finitedimensional, then it is wellknown that the diagonalizable subalgebras of $\mathrm{End}(V)$ are characterized by their internal algebraic structure: they are the subalgebras isomorphic to $K^n$ for some natural number $n$.
In case $V$ is infinite dimensional, the diagonalizable subalgebras of $\mathrm{End}(V)$ cannot be characterized purely by their internal algebraic structure: one can find diagonalizable and nondiagonalizable subalgebras that are isomorphic. I will explain how to characterize the diagonalizable subalgebras of $\mathrm{End}(V)$ as \emph{topological} algebras, using a natural topology inherited from $\mathrm{End}(V)$. I also hope to show how this characterization relates to an infinitedimensional WedderburnArtin theorem that characterizes ``topologically semisimple'' algebras.

04/14/15
Thomas Cass  Imperial College London
Tail estimates and applications for rough differential equations
AbstractConsider a solution to an ordinary differential equation driven along smooth vector fields $V=\left( V^{1},...,V^{d}\right) $ of linear growth.
\begin{equation}
dy_{t}=V\left( y_{t}\right) dx_{t},\text{ started from }y_{0}.\label{ode}%
\end{equation}
If $x$ has finite $1$variation then Gronwall's inequality gives a bound on
$y$ of the type%
\[
\left\vert y\right\vert _{1var}\leq C\exp\left( C\left\vert x\right\vert
_{1var}\right) .
\]
If $x$ has finite $p$variation for $p>2$ then rough path theory needs to be
used to understand (\ref{ode}), and a corresponding growth estimate of the
form
\[
\left\vert y\right\vert _{pvar}\leq C\exp\left( C\left\vert \mathbf{x}%
\right\vert _{pvar}^{p}\right)
\]
can be derived in some cases. For a large class of random rough paths
$\mathbf{x=x}\left( \omega\right) $, e.g. the Brownian rough path, the right
hand side of this inequality is not integrable (Fernique's theorem). This has
implications for some applications of interest, such as showing the existence
and smoothness of densities of RDEs via Malliavin calculus.In this talk we show how this obstacle can be bypassed by consideration of the
socalled \textit{accumulated pvariation }$M\left( \mathbf{x}\right) $ of a
$p$rough path $\mathbf{x}$ over $\left[ 0,t\right] $ which is given by%
\[
M\left( \mathbf{x}\right) =\sup_{\overset{D=\left\{ 0=t_{0}<t_{1}%
<...t_{r}=t\right\} }{\left\vert \left\vert \mathbf{x}\right\vert \right\vert
_{p\text{}var,\left[ t_{i},t_{i+1}\right] }\leq1}}\sum_{i=1}^{r}\left\vert
\mathbf{x}\right\vert _{p\text{}var,\left[ t_{i},t_{i+1}\right] }^{p}.
\]
We prove precise tail estimates for $M\left( \mathbf{x}\left( \omega\right)
\right) $ in two important cases: (i) general Gaussian rough paths and (ii)
the class of Markovian rough paths associated to subelliptic Dirichlet form.
This is based on joint works with, respectively, Christian Litterer and Terry
Lyons for case (i) and Marcel Ogrodnik for case (ii). 
04/14/15
Hongchao Zhang  Louisiana State University
A Fast Algorithm for Polyhedral Projection
AbstractIn this talk, we discuss a very efficient algorithm for projecting a point onto a polyhedron. This algorithm solves the projeciton problem through its dual and fully exploits the sparsity. The SpaRSA (Sparse Reconstruction by Separable Approximation) is used to approximately identify active constraints in the polyhedron, and the Dual Active Set Algorithm (DASA) is used to compute a high precision solution. Some interesting convergence properties and very promising numerical results compared with the stateoftheart software IPOPT and CPLEX will be discussed in this talk.

04/14/15
Guoce Xin  Center for Combinatorics, Nankai University
The theory of Constant Term Identities with applications to Combinatorics.
AbstractThis will be the second in a series of talks on the theory of evaluating constant term identities and their applications to combinatorics and algebra.

04/16/15
Cal Spicer  UCSD
Mumford's Treasure Map
AbstractThis will be a laid back introduction to affine schemes, one of the basic objects of study of modern algebraic geometry. Primarily, we will explore some simple and concrete examples, which will motivate the otherwise abstract theory. Finally, we will give a description of the arithmetic surface, and showcase David Mumford's intimate and revealing portrait of $\text{Spec}(\mathbb{Z}[X])$. No knowledge is assumed beyond a vague recollection of what a ring is.

04/16/15
Joachim Dzubiella  Soft Matter Physics, Helmholtz Center, Berlin, Germany
Curvature Dependence of Hydrophobic Hydration Dynamics
AbstractWe investigate the curvaturedependence of water dynamics in the vicinity of hydrophobic spherical solutes using molecular dynamics simulations. For both, the lateral and perpendicular diffusivity as well as for Hbond kinetics of water in the first hydration shell, we find a nonmonotonic solutesize dependence, exhibiting extrema close to the wellknown structural crossover length scale for hydrophobic hydration. Additionally, we find an apparently anomalous diffusion for water moving parallel to the surface of small solutes, which, however, can be explained by topology effects. The intimate connection between solute curvature, water structure and dynamics has implications for our understanding of hydration dynamics at heterogeneous biomolecular surfaces.

04/16/15
Rene Schoof  Universita di Roma Tor Vergata
Finite group schemes and abelian varieties with good reduction outside one prime
AbstractThe Jacobian $J_0(23)$ of the modular curve $X_0(23)$ is a semistable abelian variety over $\Bbb Q$ with good reduction outside $23$. It is simple. We prove that every simple semistable abelian variety over $\Bbb Q$ with good reduction outside $23$ is isogenous over $\Bbb Q$ to $J_0(23)$.

04/21/15
Palina Salanevich  Jacobs University
Polarization Based Phase Retrieval for TimeFrequency Structured Measurements
AbstractIn many areas of imaging science, such as diffraction imaging, astronomical imaging, microscopy, etc., optical detectors can often only record the squared modulus of the Fraunhofer or Fresnel diff raction pattern of the radiation that is scattered from an object. In such setting, it is not possible to measure the phase of the optical wave reaching the detector. So, it is needed to reconstruct a signal from intensity measurements only. This problem is called phase retrieval.
We are going to consider the case when the measurement frame is a Gabor frame, that is, the case of timefrequency structured measurements. The main motivation is that in this case, the frame coefficients are of the form of masked Fourier coefficients, where the masks are time shifts of the Gabor window. This makes measurements meaningful for applications, but at the same time preserves the flexibility of the frametheoretic approach. The most efficient existing algorithms, such as PhaseLift, work with randomly generated Gaussian frames. I am going to present the recovery algorithm with a sufficiently small number of measurements required, which is working with timefrequency structured measurements. The algorithm is based on the idea of polarization, first proposed by Alexeev, Bandeira, Fickus and Mixon. 
04/21/15
Adriano Garsia  UCSD
The theory of constant term identities with applications to combinatorics III

04/23/15
Thomas Murphy  CSU Fullerton
Spectral Geometry of toric Einstein manifolds
AbstractThe eigenvalues of the Laplacian encode fundamental geometric information
about a Riemannian metric. As an example of their importance, I will
discuss how they arose in work of Cao, Hamilton and Illmanan, together
with joint work with Stuart Hall, concerning stability of Einstein
manifolds and Ricci solitons. I will outline progress on these problems
for Einstein metrics with large symmetry groups. We calculate bounds on
the first nonzero eigenvalue for certain HermitianEinstein four
manifolds. Similar ideas allow us estimate to the spectral gap (the
distance between the first and second nonzero eigenvalues) for any toric
KaehlerEinstein manifold M in terms of the polytope associated to M. I
will finish by discussing a numerical proof of the instability of the
ChenLeBrunWeber metric. 
04/23/15
Shaoying (Kathy) Lu  UCSD, Bioengineering
Imagedriven Analysis of Molecular Transport and Activation in Single Live Cells
AbstractGenetically encoded biosensors based on fluorescence resonance energy transfer (FRET) have been widely applied to visualize the molecular activity in live cells with high spatiotemporal resolution. However, the rapid diffusion of biosensor proteins hinders a precise reconstruction of the actual molecular activation map. Based on fluorescence recovery after photobleaching (FRAP) experiments, we have developed a finite element (FE) method to analyze, simulate, and subtract the diffusion effect of mobile biosensors. This method has been applied to analyze the mobility of Src FRET biosensors engineered to reside at different subcompartments in live cells. The results indicate that the Src biosensor located in the cytoplasm moves 48 folds faster than those anchored on different compartments in plasma membrane. The mobility of biosensor at lipid rafts is slower than that outside of lipid rafts and is dominated by twodimensional diffusion. When this diffusion effect was subtracted from the FRET ratio images, high Src activity at lipid rafts was observed at clustered regions proximal to the cell periphery, which remained relatively stationary upon epidermal growth factor (EGF) stimulation. This result suggests that EGF induced a Src activation at lipid rafts with wellcoordinated spatiotemporal patterns. Our FEbased method also provides an integrated platform of image analysis for studying molecular motility and reconstructing the spatiotemporal activation maps of signaling molecules in live cells. Furthermore, we developed a correlative FRET imaging microscopy (CFIM) approach to quantitatively analyze the subcellular coordination between the enzymatic activity and the structural focal adhesion (FA) dynamics. By CFIM, we found that different FA subpopulations have distinctive regulation mechanisms controlled by local kinase activity. Therefore, our work highlights the importance of dynamic single livecell imaging and its integration indepth mathematical analysis.

04/23/15
Majid Hajian  California Institute of Technology
On a motivic method in Diophantine geometry
AbstractBy studying variation of motivic path torsors associated to a variety, we show how certain nondensity assertions in Diophantine geometry can be translated to problems concerning Kgroups. Concrete results then follow based on known (and conjectural) vanishing theorems.

04/24/15
Dan Hoff  UCSD
A Class of von Neumann Algebras Which Admit Unique Prime Factorization
AbstractA tracial von Neumann algebra $M$ is called prime if it cannot be decomposed as the tensor product of two nontrivial (not type ${\rm I}$) subalgebras. Naturally, if $M$ is not prime, one asks if $M$ can be uniquely factored as a tensor product of prime subalgebras. The first result in this direction is due to Ozawa and Popa in 2003, who gave a large class of groups $\mathcal{C}$ such that for any $\Gamma_1, \dots, \Gamma_n \in \mathcal{C}$, the associated von Neumann algebra $L(\Gamma_1) \otimes \cdots \otimes L(\Gamma_n)$ is uniquely factored. This talk will focus on von Neumann algebras arising from a class of measured equivalence relations, and how the techniques of Ozawa and Popa can be adapted to this setting.

04/28/15
Jeremy Schmitt  UCSD
Taylor Variational Integrators
AbstractA brief introduction to discrete variational mechanics, motivated by the goal of constructing symplectic onestep methods, will be presented. Followed by the presentation of a new type of variational integrator that utilizes Taylor's method in it's construction. Time permitting, we will make some remarks on the pros/cons and stability of constructing the variational integrator from the Lagrangian variational framework versus the Hamiltonian variational framework.

04/28/15
Marino Romero  UCSD
The theory of constant term identities with applications to combinatorics IV.

04/30/15
Tianyi Zheng  Stanford University
Random walks and isoperimetric profiles of groups
AbstractAsymptotic behavior of random walks on a group, such as decay of return probability and growth of entropy, reflects large scale geometry of the underlying group. The notion of isoperimetric profiles, motivated by classical isoperimetric inequalities and FaberKrahn inequalities, captures useful geometric information that affects behavior of random walks. In this talk I will explain some interesting examples of groups acting on trees, where random walks exhibit rich exotic behavior. A connection between return probability lower bound and entropy growth will also be discussed.

04/30/15
Michelle Bodnar  UCSD
Greedy algorithms and Matroids
AbstractGreedy algorithms are a popular choice for solving problems because they are often simple, intuitive, and efficient. However, they can also be misleading, sometimes yielding the worst possible solution to a problem. In this talk we'll go through some examples of greedy algorithms (we'll look at the best example first, and go from there) and discuss when they perform terribly, optimally, and when we can bound how close the greedy solution is to the optimal solution. Finally, we'll review what matroids are and prove that a greedy algorithm yields an optimal solution to a particular class of problems if and only if we can rephrase the problem as a statement about a matroids.
Sponsored by the GSA.

04/30/15
Johanna Hennig  UCSD
Locally finite dimensional Lie algebras

04/30/15
Grzegorz Banaszak  Adam Mickiewicz University in Poznan
The algebraic SatoTate group and Sato Tate conjecture
AbstractLet $K$ be a number field and let $A$ be an abelian variety over $K$. In an effort of proper setting of the SatoTate conjecture concerning the equidistribution of Frobenius elements in the representation of the Galois group $G_K$ on the Tate module of $A$, one of attempts is the introduction of the algebraic SatoTate group
$AST_{K}(A)$. Maximal compact subgroups of $AST_{K}(A)(\mathbb{C})$ are
expected to be the key tool for the statement of the SatoTate conjecture for $A$. At the lecture, following an idea of JP. Serre, an explicit construction of $AST_{K}(A)$ will be presented based on P. Deligne's motivic category for absolute Hodge cycles. I will discuss the arithmetic properties of $AST_{K}(A)$ along with explicit computations of $AST_{K}(A)$ for some families of abelian varieties. I will also explain how this construction extends to absolute Hodge cycles motives in the Deligne's motivic category for absolute Hodge cycles. This is joint work with Kiran Kedlaya. 
04/30/15
Rene Schoof  Universita di Roma Tor Vergata
Elliptic curves and modular curves
AbstractIn 1972 J.P. Serre proved an important theorem concerning the Galois action on the torsion points of elliptic curves over number fields. We describe a conjectural uniform version of this theorem and its relation to rational points on modular curves.
May

05/01/15
Ming Xiao  Rutgers University/UIUC
Nonembeddability into a Fixed Sphere for a Family of Compact Real Algebraic Hypersurfaces.
AbstractWe study the holomorphic embedding problem from a compact real algebraic hypersurface into a sphere. By our theorem, for any integer $N$, there is a family of compact real algebraic strongly pseudoconvex hypersurfaces in $C^2$ , none of which can be locally holomorphically embedded into the unit sphere in $C^N$. This shows that the Whitney (or Remmert) type embedding theorem in differential topology(or in the Stein space theory, respectively) does not hold in the setting above. This is a joint work with Xiaojun Huang and Xiaoshan Li.

05/05/15
Marino Romero  UCSD
The theory of constant term identities with applications to combinatorics V.

05/07/15
Kavita Ramanan  Brown University
Obliquely reflected diffusions in nonsmooth domains
AbstractObliquely reflected diffusions in smooth domains are classical objects that have been well understood for half a century. On the other hand, many fundamental questions remain in the study of reflected diffusions in nonsmooth domains, which arise in a variety of fields ranging from mathematical physics to stochastic networks. We first describe some recent results on reflected diffusions in piecewise smooth domains. We then introduce a new approach to the construction and characterization of obliquely reflected Brown motions in bounded, simply connected planar domains. The class of processes we construct also includes certain processes with jumps that have arisen in the study of SLE. This talk is partially based on joint works with Chris Burdzy, Zhenqing Chen, Weining Kang and Donald Marshall.

05/07/15
Tatiana Bandman  BarIlan University
Surjectivity and equidistribution of word maps on $\operatorname{SL}(2)$ and $\operatorname{PSL}(2)$.
AbstractLet $w = \prod x^{a_i} y^{b_i}$ be an element of a free group on two generators $x, y$. For every group $G$ the corresponding word map $w : G^2 \to G$ is defined as $w(g_1, g_2) = \prod g_1^{a_1} g_2^{a_2}$. I will speak about surjectivity and equidistribution of such word maps on groups $\operatorname{PSL}(2)$ and $\operatorname{SL}(2)$. This is a report on the joint works with Sh. Garion, F. Grunewald, B.Kunyavskii, Eu. Plotkin, and N. Gordeev.

05/07/15
Yuri Zarhin  Penn State University
Tate and Weil classes on abelian varieties over finite fields
AbstractWe discuss nontrivial multiplicative relations among eigenvalues of Frobenius endomorphisms of abelian varieties over finite fields. (The trivial relations are provided by the Riemann Hypothesis that was proven by A. Weil.) We classify all abelian varieties over finite fields of a certain dimension which admit the nontrivial relations and give an explicit construction of corresponding exotic Tate classes.

05/07/15
Gary Huber  UCSD, Biochemistry & HHMI
BrownDye: Software for Performing Brownian Dynamics on Biological Molecules
AbstractOne of the main challenges of computational biology is predicting the rate constants of association and dissociation of large molecules. In order to make the computations feasible, simplifying assumptions are made that still allow essential features of the physical process to be captured. Discussion will include current and upcoming features of the software as well as the physics and algorithms involved.

05/07/15
Yuri Zarhin  Penn State University
Finite automorphism groups of algebraic varieties
AbstractA classical theorem of Jordan asserts that every finite subgroup $B$ of the complex general linear (matrix) group $GL(n)$ contains an abelian (normal) subgroup $A$ such that the index of $A$ in $B$ does not exceed a universal constant that depends only on $n$. We discuss analogues of Jordan's theorem where the matrix group is replaced by the group of biregular (or birational) automorphisms of a complex algebraic variety, or by the diffeomorphism group of a smooth real manifold.

05/08/15
Johanna Hennig  UCSD
Path algebras of quivers and representations of locally finite Lie algebras
AbstractWe explore the (noncommutative) geometry of representations of locally finite Lie algebras. Let L be one of these Lie algebras, and let I in U(L) be the annihilator of a locally simple Lmodule. We show that for each such I, there is a quiver Q so that locally simple Lmodules with annihilator I are parameterized by "points" in the "noncommutative space" corresponding to the path algebra of Q. We classify the quivers that occur and along the way discover a beautiful connection to characters of the symmetric groups $S_n$.

05/11/15
Zonglin Jiang  UCSD
On the Geometric Satake Isomorphism

05/12/15
Mark Iwen  Michigan State University
Fast Phase Retrieval for HighDimensions
AbstractCertain imaging applications such as xray crystallography require the recovery
of an underlying signal from intensity (or magnitude) measurements  a problem
commonly referred to as Phase Retrieval. In this talk, we discuss a framework for
solving the discrete phase retrieval problem using block circulant measurement
constructions and angular synchronization. We develop an algorithm which is
nearlinear time, making it computationally feasible for large dimensional
signals. Theoretical and experimental results demonstrating the method's
speed, accuracy and robustness will be presented. We also present an extension
of the framework to sparse phase retrieval, including the first known
sublineartime compressive phase retrieval algorithm. 
05/14/15
Daniel Smith  UCSD
Kodaira Vanishing and Formal Schemes
AbstractI will give an overview of Kodaira's vanishing theorem and its applications in higherdimensional algebraic geometry. I will then proceed to give an introduction to formal schemes and their applications. Then I will state a version of the vanishing theorem for formal schemes, along with some possible further results to be investigated.

05/14/15
Todd Kemp  UCSD
The Hard Edge of Unitary Brownian Motion
AbstractRandom matrix theory is filled with laws of large numbers and central limit theorems, all specialized to different statistics and scaling regimes. The two most famous laws of large numbers are for Gaussian Wigner (Hermitian) matrices: the bulk (empirical distribution) of eigenvalues converge a.s. to the semicircle law, and the largest eigenvalue converges to twice the common variance of the entries. The corresponding central limit theorems give Gaussian fluctuations in the bulk, but a completely different distribution (the TracyWidom Law) for the largest eigenvalue.
One can view a Gaussian Wigner matrix as (a marginal of) Brownian motion on the Lie algebra of Hermitian matrices. It is then natural to study the analogous questions for the eigenvalues of the Brownian motion on the associated Lie group: the unitary group. For the bulk, the a.s. limit empirical eigenvalue distribution was discovered by Biane and Rains independently in the late 1990s; the corresponding bulk central limit result was largely found by L\'evy and Ma\"ida in 2010

05/14/15
Andy Wilson  UCSD
The Ubiquity of Elliptic Curves
AbstractElliptic curves appear prominently in Wiles's resolution of Fermat's Last Theorem, the Birch and SwinnertonDyer Conjecture (a Millennium Problem), and Lenstra's factoring algorithm, and they are also important in modern cryptography. In this talk, we will give a gentle introduction to elliptic curves and then explain some of these applications without assuming any background in algebraic geometry or number theory.
Sponsored by the GSA.

05/14/15
Amir Babak Aazami
Contact and symplectic structures on closed Lorentzian manifolds
AbstractWe investigate timelike and null vector flows on closed Lorentzian manifolds and their relationship to Ricci curvature. The guiding observation, first observed for closed Riemannian 3manifolds by Harris & Paternain '13, is that positive Ricci curvature tends to yield contact forms, namely, 1forms metrically equivalent to unit vector fields with geodesic flow. We carry this line of thought over to the Lorentzian setting. First, we observe that the same is true on a closed Lorentzian 3manifold: if X is a global timelike unit vector field with geodesic flow satisfying $Ric(X,X) > 0$, then $g(X,â€¢)$ is a contact form with Reeb vector field X, at least one of whose integral curves is closed. Second, we show that on a closed Lorentzian 4manifold, if X is a global null vector field satisfying $\nabla_XX = X$ and $Ric(X) > divX  1$, then $dg(X,â€¢)$ is a symplectic form and X is a Liouville vector field.

05/14/15
Jiayi Wen  UCSD
Mathematical Modeling and Computational Methods for Electrostatic Interactions with Application to Biological Molecules
AbstractElectrostatic interactions play an important role in many complex charged systems, such as biological molecules, soft matter material, nanofluids, and electrochemical devices. In this work, we develop mathematical theories and computational methods to understand such interactions, particularly in charged biological molecular systems. Our main contributions include: 1. Theoretical studies of meanfield variational models of ionic solution and that of molecular surfaces with the PoissonBoltzmann electrostatics; 2. Design and implementation of the corresponding computational algorithms, and conduct extensive Monte Carlo simulations and numerical solutions of partial differential equations for chargecharge interactions; 3. Discovery of various interesting properties of charged molecules, validate some experimental results, and clarify some confusion in literature. A common theme of this work is the variational approach. Many physical effects such as ionic size effects, solvent entropy, concentration dependent dielectric response can be incorporated into a meanfield freeenergy functional of ionic concentrations coupled with the Poisson equation for electrostatics. The techniques of analysis developed in this work may help improve the understanding of the underlying physical properties of charged systems and provide new ways of studying analytically and numerically other problems in the calculus of variations.

05/14/15
Mihai Putinar  UCSB
Matrix positivity preservers in fixed dimension
AbstractA celebrated 1942 result of Schoenberg characterizes all entrywise functions which preserve positivity of matrices of any size. I will present a characterization of polynomials which preserve positivity when applied entrywise on matrices of a fixed dimension. All put in historical context and motivated by recent demands of statistics of large data and optimization theory. A sketch of the proof will take a detour through the representation theory of the symmetric group.

05/15/15
Matthew Kerr  Washington University, St. Louis
Normal functions and locally symmetric varieties
AbstractAn algebraic cycle homologous to zero on a variety leads to an
extension of Hodgetheoretic data, and in a variational context to a
family of extensions called a normal function. These may be viewed as
"horizontal" sections of a bundle of complex tori, and are used to detect
cycles modulo algebraic (or rational) equivalence. Conversely, the
existence of normal functions can be used to predict that interesting
cycles are present... or absent: a famous theorem of Green and Voisin
states that for projective hypersurfaces of large enough degree, there are
no normal functions (into the intermediate Jacobian bundle associated to
these hypersurfaces) over any etale neighborhood of the coarse moduli
space. Inspired by recent work of FriedmanLaza on Hermitian variations of
Hodge structure and Oort's conjecture on special (i.e. Shimura)
subvarieties in the Torelli locus, R. Keast and I wondered about the
existence of normal functions over etale neighborhoods of Shimura
varieties. Here the function is supposed to take values in a family of
intermediate Jacobians associated to a representation of a reductive
group. In this talk I will explain our classification of the cases where a
GreenVoisin analogue does *not* hold and where one therefore expects
interesting cycles to occur, and give some evidence that these predictions
might be "sharp". 
05/19/15
Jiri Lebl  Oklahoma State University
Extensions of CR functions in ${\mathbb C}^n \times {\mathbb R}$
AbstractThis is joint work with Alan Noell and Sivaguru Ravisankar. We prove a HartogsBochner type theorem for a bounded domain $U$ with smooth boundary in ${\mathbb C}^n \times {\mathbb R}$ with nodegenerate, flat, and elliptic CR singularities (all natural conditions for the problem). That is, a CR function on the boundary $\partial U$ extends to a CR function on $U$, smooth up to the boundary.

05/21/15
Alan Hammond  UC Berkeley
Selfavoiding polygons and walks: counting, joining and closing.
AbstractSelfavoiding walk of length n on the integer lattice $Z^d$ is the uniform measure on nearestneighbour walks in $Z^d$ that begin at the origin and are of length $n$. If such a walk closes, which is to say that the walk's endpoint neighbours the origin, it is natural to complete the missing edge connecting this endpoint and the origin. The result of doing so is a selfavoiding polygon. We investigate the numbers of selfavoiding walks, polygons, and in particular the "closing" probability that a length n selfavoiding walk is closing. Developing a method (the "snake method") employed in joint work with Hugo DuminilCopin, Alexander Glazman and Ioan Manolescu that provides closing probability upper bounds by constructing sequences of laws on selfavoiding walks conditioned on increasing severe avoidance constraints, we show that the closing probability is at most $n^{1/2 + o(1)}$ in any dimension at least two. Developing a quite different method of polygon joining employed by Madras in 1995 to show a lower bound on the deviation exponent for polygon number, we also provide new bounds on this exponent. We further make use of the snake method and polygon joining technique at once to prove upper bounds on the closing probability below $n^{1/2}$ in the twodimensional setting.

05/21/15
Hui Sun  UCSD, Math/Biochem
Numerical Simulation of Solvent Stokes Flow and SoluteSolvent Interface Dynamics
AbstractFundamental biological molecular processes, such as protein folding, molecular recognition, and molecular assemblies, are mediated by surrounding aqueous solvent (water or salted water). Continuum description of solvent is an efficient approach to understanding such processes. In this work, we develop a solvent fluid model and computational methods for solvent dynamics and solutesolvent interface motion. The key components in our model include the Stokes equation for the incompressible solvent fluid which governs the motion of the solutesolvent interface, the idealgas law for solutes, and the balance on the interface of viscous force, surface tension, van der Waals type dispersive force, and electrostatic force. We use the ghost fluid method to discretize the flow equations that are reformulated into a set of Poisson equations, and design special numerical boundary conditions to solve such equations to allow the change of solute volume. We move the interface with the levelset method. To stabilize our schemes, we use the Schur complement and leastsqures techniques. Numerical tests in both two and threedimensional spaces will be shown to demonstrate the convergence of our method, and to demonstrate that this new approach can capture dry and wet hydration states as observed in experiment and molecular dynamics simulations.

05/21/15
Chenxu Wen  Vanderbilt University
Unique Maximal Amenable Extension of the Radial MASA in the Free Group Factor
AbstractTwo of the most important examples in $II_1$ factors are the amenable $II_1$ factor and the free group factors. The first one is wellunderstood, thanks to Connes' fundamental work, while the structure of free group factors is still under intense study. Regarding amenable subalgebras inside free group factors, Jesse Peterson conjectured that any diffuse amenable subalgebra of a free group factor has a unique maximal amenable extension. In this talk I will show that any diffuse subalgebra of the radial masa in a free group factor with finitely many generators, has a unique maximal amenable extension.

05/21/15
Piotr Krason  Szczecin University, Poland
On arithmetic in MordellWeil groups
AbstractWe will describe the problem of detecting linear dependence of points in MordellWeil groups A(F) of abelian varieties. This is done via reduction maps. We determine the sufficient conditions for the reduction maps to detect linear dependence in A(F).
We also show that our conditons are very close to be or perhaps are the best possible. In particular we try to determine the conditions for detecting linear dependence in MordellWeil groups via finite number of reductions. The methods combine applications of transcedental, ladic and mod v techniques. This is joint work with G. Banaszak. 
05/22/15
Laura Geatti  Rome
Envelopes of holomorphy in the complexification of a Riemannian symmetric space
AbstractLet $G/K$ be a Riemannian symmetric space. Its complexification $G^C / K^C$ is a Stein manifold, and lefttranslations by $G$ are holomorphic transformations of $G^C / K^C$. In this setting, invariant domains and their envelopes of holomorphy are natural objects of study. If $G/K$ is compact, then every invariant domain $D$ in $G^C / K^C$ intersects a complex torus orbit in a lower dimensional Reinhardt domain $\Omega_D$. In this case, complex analytic properties of $D$ can be expressed in terms of those of $\Omega_D$. If $G/K$ is a noncompact, then the situation is fully understood only in the rankone case. In this talk we present some univalence results for the envelope of holomorphy of a $G$invariant domain in $G^C / K^C$, when the space $G/K$ is a noncompact Hermitian symmetric space (joint work with A. Iannuzzi).

05/26/15
Mark Kempton
Higher Dimensional Spectral Graph Theory

05/26/15
Sorin Dragomir  Potenza, Italy
CauchyRiemann Structures, Lorentzian Geometry and Subelliptic Theory

05/27/15
Andy Wilson
Generalized shuffle conjectures for the GarsiaHaiman delta operator
AbstractWe conjecture two combinatorial interpretations for a symmetric function arising from an eigenoperator on the Macdonald polynomials called the delta operator. Both interpretations generalize the famous Shuffle Conjecture, which connects these eigenoperators to parking functions. We prove several cases of these new conjectures using objects such as ordered set partitions, rook placements, Tesler matrices, and LLT polynomials. In particular, we obtain an extension of MacMahon's classical equidistribution theorem from permutations to ordered set partitions, which was described in the speaker's advancement to candidacy.

05/28/15
Lucian Beznea  Bucharest
Measurevalued branching processes of Dirichlet and Neumann nonlinear boundary value problems.
Jun

06/02/15
Xing Peng  UCSD
On the decomposition of random hypergraphs
AbstractFor an $r$uniform hypergraph $H$, let $f(H)$ be the minimum number of complete $r$partite $r$uniform subhypergraphs of $H$ whose edge sets partition the edge set of $H$.
In this talk, I will discuss the value of $f(H)$ for the random hypergraph $H$. Namely, I will prove that if $(\log n)^{2.001}/n \leq p \leq 1/2$ and $H \in H^{(r)}(n,p)$, then with high probability $f(H)=(1\pi(K^{(r1)}_r)+o(1))\binom{n}{r1}$, where $\pi(K_{r}^{(r1)})$ is the Tur\'an density of $K_{r}^{(r1)}$. 
06/04/15

06/04/15
Piotr Grazcyk  LAREMA, Universite d'Angers
SDEs for particle systems and applications in harmonic analysis
AbstractConsider the following system of SDEs $d\lambda_i = \sigma_i(\lambda_i)dB_i+\left(b_i(\lambda_i)+\sum_{j\neq i}\frac{H_{ij}(\lambda_i,\lambda_j)}{\lambda_i\lambda_j}\right)dt\/,\quad i=1,\ldots,p\/$, (1)
describing ordered particles $\lambda_1(t)\leq \ldots\leq \lambda_p(t)$, $t\geq0$ on $R$. Here $B_i$ denotes a collection of onedimensional independent Brownian motions.Let $Sym(p\times p)$ be the vector space of symmetric real $p\times p$ matrices. The SDEs systems (1) contain the systems describing, for the starting point having no collisions, the eigenvalues of the $Sym(p\times p)$valued process $X_t$ satisfying the following matrix valued stochastic differential equation $dX_t = g(X_t)dW_th(X_t)+h(X_t)dW_t^Tg(x_t)+b(X_t)dt\/$, where the functions $g,h,b$ act spectrally on $Sym(p\times p)$, and $W_t$ is a Brownian matrix of dimension $p\times p$. Thus the systems (1) contain Dyson Brownian Motions, Squared Bessel particle systems, their $\beta$versions and other particle systems crucial in mathematical physics and physical statistics.
Note that the functions $\displaystyle{\frac{H_{ij}(lambda_i, \lambda_j)}{\lambda_i\lambda_j}}$ describe the repulsive forces with which the particle $\lambda_i$ acts on the particle $\lambda_j$. On the other hand the singularities $\displaystyle{\frac{1}{\lambda_i\lambda_j}}$ make the SDEs system (1) difficult to solve, especially when the starting point $\Lambda(0)$ has a collision $\lambda_i(0)= \lambda_j(0)$. The most degenerate case $\lambda_1(0)= \ldots= \lambda_p(0)$ is of great importance in applications.
In some particular cases (Dyson Brownian Motions, some Squared Bessel particle systems), the existence of strong solutions of (1) has been established by C\'epa and L\'epingle, using the technique of Multivalued SDEs.
We prove the existence of strong and pathwise unique noncolliding solutions of (1), with a degenerate colliding initial point $\Lambda(0)$ in the whole generality, under natural assumptions on the coefficients of the equations in (1). Our approach is based on the classical It\^o calculus, applied to elementary symmetric polynomials in $p$ variables $X=(x_1, \ldots,x_p)$
$e_n(X) = \sum_{i_1<\ldots<i_n}x_{i_1}x_{i_2}\ldots x_{i_n}\/$,
as well as to symmetric polynomials of squares of differences between particles $V_n = e_n(A)\/,\quad \textrm{where } A = \{a_{ij}=(\lambda_i\lambda_j)^2:1\leq i<j\leq p\}\/$.
In the case of Squared Bessel particle systems $d\lambda_i = 2\sqrt{\lambda_i}dB_i+ \left(\alpha+\sum_{j\neq i}\frac{\lambda_i+\lambda_j}{\lambda_i\lambda_j}\right)dt\/$, describing the eigenvalues of the matrix Squared Bessel process $dX_t = \sqrt{X_t}dW_t+dW_t^T\sqrt{X_t+}\alpha I dt\/$, we use our stochastic approach in order to determine the socalled Wallach set of permissible parameters $\alpha$, known before only by harmonic analysis methods. We also determine the admissible starting points of such processes for $\alpha=1,\ldots, p2$.

06/04/15
Nordine Mir  TAMU, Qatar
On the analytic regularity of CR maps of positive codimension
AbstractIn this talk, we shall describe some recent new results about analyticity of CR maps of positive codimension, generalizing a number of earlier results in the field.

06/04/15
Christopher Tiee
Applications of Finite Element Exterior Calculus to Evolution Problems
AbstractGeometry has been, in recent times, a great inspiration for mathematical problems. It is therefore useful to consider numerical methods in effort to visualize and explore properties of the solutions to the partial differential equations arising from these problems. We examine a modern framework, Hilbert complexes, which abstracts many of the essential details relevant for partial differential equations, such as exterior derivatives and coderivatives, Laplacians, and PoincarÃ© inequalities. This viewpoint also proves useful for approximation via the finite element method. We prove some abstract error estimates and apply these results to the case of numerically computing parabolic equations on Riemannian hypersurfaces.

06/04/15
Shenggao Zhou  UCSD, Math and Biochemistry
Incorporation of Solvent Fluctuations into Variational ImplicitSolvent Model
AbstractSolvent fluctuations play a fundamental role in many watermediated molecular interactions. The significance of an efficient implicitsolvent model that can capture solvent fluctuations cannot be overemphasized. In this talk, solvent fluctuations are incorporated into a variational implicitsolvent model in two different approaches. In the first approach, solutesolvent interface fluctuations are taken into account by using a stochastic level set method with noises in the normal velocity. Numerical simulations show that the method can capture dewetting transitions of hydrophobic confinements and can estimate the activation energy barrier of such transitions. The other approach employs a binary levelset representation of the solute and solvent regions. The solvent fluctuation is incorporated through Isingtype Monte Carlo flips of the binary levelset values. Coupled with solute fluctuations, this approach is able to study the folding and unfolding processes of a hydrophobic polymer. Some preliminary results are presented.

06/04/15
Janine LoBue Tiefenbruck
Combinatorial Properties of Quasisymmetric Schur Functions and Generalized Demazure Atoms
AbstractWe present new MurnaghanNakayama rules for certain refinements of the Schur functions, the quasisymmetric Schur functions and the generalized Demazure atoms. We also briefly explore the enumeration of the combinatorial objects called permuted basement fillings that generate the generalized Demazure atoms.

06/05/15
Howard Nuer  Rutgers University
Moduli spaces of stable sheaves on an Enriques surface
AbstractWhile stable sheaves on surfaces with trivial canonical bundle, i.e. K3 or Abelian surfaces, have been extensively studied, the Enriques case is much less understand. We will first discuss the past work of Kim, Hauzer, and Yoshioka on some existence and irreducibility results, and then present our new results which give necessary and sufficient conditions for the existence of stable sheaves with prescribed chern classes. Furthermore, we will discuss some new irreducibility results as well as some of the geometry of these moduli spaces. Time permitting, we will describe a near complete ongoing project describing the MMP of these moduli spaces using Bridgeland stability techniques.

06/08/15
James Eldred Pascoe
Boundary behavior of Pick functions in several variables

06/08/15
Cyril Houdayer  Universite ParisEst MarnelaVallee
Asymptotic structure and rigidity of free product von Neumann algebras
AbstractI will give an overview of recent results obtained in joint work with Yoshimichi Ueda on the structure and the rigidity of arbitrary free product von Neumann algebras. First, I will explain that in any free product von Neumann algebra, any amenable von Neumann subalgebra that has a diffuse intersection with one of the free components is necessarily contained in this free component. This result completely settles the problem of maximal amenability inside free product von Neumann algebras. Then I will present new Kuroshtype rigidity results for free product von Neumann algebras. Namely, I will explain that for any family of nonamenable factors belonging to a large class of (possibly type III) factors including nonprime factors, nonfull factors and factors with a Cartan subalgebra, the corresponding free product von Neumann algebra with respect to arbitrary states retains the cardinality of the family as well as each factor up to unitary conjugacy, after permutation of the indices.

06/11/15
Francesco Baldassari  Universita degli Studi di Padova
A $p$adically entire function with integral values on $\mathbb{Q}_p$ and the exponential of perfectoid fields
Abstract\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
We give an essentially selfcontained proof of the fact that a certain
$p$adic power series
$$
\Psi= \Psi_p(T) \in T + T^{2}\Z[[T]]\;,
$$
which trivializes the addition law of the formal group of Witt
$p$covectors $\widehat{\rm CW}_{\Z}$, is $p$adically entire and
assumes values in $\Z_p$ all over $\Q_p$. We also carefully examine its
valuation and Newton polygons. We will recall and use the isomorphism
between the Witt and hyperexponential groups over $\Z_p$, and the
properties of $\Psi_p$, to show that, for any
perfectoid field extension $(K,\,)$ of $(\Q_p,\,_p)$, and to a
choice of a pseudouniformizer $\varpi = (\varpi^{(i)})_{i \geq 0}$ of
$K^\flat$, we can associate a continuous additive character
$\Psi_{\varpi}: \Q_p \to 1+K^{\circ \circ}$, and we will give a formula
to calculate it. The character $\Psi_{\varpi}$ extends the map $x
\mapsto \exp \pi x$, where
$$\pi := \sum_{i\geq 0} \varpi^{(i)} p^i + \sum_{i<0}
(\varpi^{(0)})^{p^{i}} p^i \in K\;.
$$
I will also present numerical computation of the first coefficients of
$\Psi_p$, for small $p$, due to M. Candilera. 
06/12/15
Jesus MartinezGarcia  JHU
On the moduli space of cubic surfaces and their anticanonical divisors
AbstractWe study variations of GIT quotients of log pairs (X,D) where X is a hypersurface of some fixed degree and D is a hyperplane section. GIT is known to provide a finite number of possible compactifications of such pairs, depending on one parameter. Any two such compactifications are related by birational transformations. We describe an algorithm to study the stability of the Hilbert scheme of these pairs, and apply our algorithm to the case of cubic surfaces. Finally, we relate this compactifications with the (conjectural) moduli space of log Ksemistable pairs.
This is work in progress with Patricio Gallardo (University of Georgia).

06/12/15
Michael McQuillan  Rome (Tor Vegata)
Failure of smooth base change for etale homotopy
AbstractAppearances not withstanding this is a talk about rational curves because they're the cause of the failure. Similarly, since homotopy groups are constant on the fibres of topological fibrations, a counterexample has to be in positive or mixed characteristic, and the specific one which I'll discuss is bidisc quotients over Spec
Z. The example also has considerable logical implications for studying boundedness of rational curves on surfaces of general type, i.e. it cannot be implied by any theorem in $ACF_0$. Conversely, and more substantially, this boundedness can be proved uniformly in sufficiently large primes $p$ in $ACF_0$ provided the surface enjoys $c_1^2> c_2$. 
06/22/15
Michel Buck  Northeastern University, Department of Physics
An overview of causal sets
AbstractCausal set theory is an approach to quantum gravity based on the idea that spacetime is fundamentally discrete and Lorentz invariant. Structurally, a causal set is a locally finite partial order, or a transitive DAG (directed acyclic graph). After a brief introduction to the idea, I will give an overview of some of the recent research activity in causal sets. Some topics I hope to touch on are: measures of discrete geometry (e.g. distance, curvature,â€¦), dynamics on causal sets (e.g. classical and quantum fields), and phenomenology from causal sets (e.g. dark energy).

06/22/15
Ian Jubb  Imperial College London, Department of Physics
Boundary Terms for Causal Sets
AbstractIn Causal Set theory the ordering of the spacetime "atoms" and their number are meant to give us all of the geometrical information. Thus, we should be able to construct causal set expressions that give us back particular geometrical quantities. In this talk I will describe a recent result that allows one to determine the GibbonsHawkingYork (GHY) boundary term for a causal set. The GHY term appears in the action for a spacetime with a boundary, and is simply the integral over the extrinsic curvature of that boundary. A side effect of the work behind this result was the emergence of a new way to calculate the dimension of a causal set. Finally, I would like to discuss the boundary contributions that are "hidden" in the bulk action for a causal set.

06/24/15
Stephen Jordan  NIST
Black holes, causality, and Grover Search
AbstractModifications to quantum mechanics have been proposed as potential solutions to the black hole information paradox. In particular, Maldecena and Horowitz have proposed a finalstate projection model in which the black hole singularity constitutes a boundary to spacetime with an associated boundary condition for the wavefunction. This proposal has gained renewed interest in light of the AMPS "firewalls" argument. We examine the computational and informationtheoretic implications of small deviations from unitarity that can arise in this model. We find that any nonunitarity allows signalling over arbitrary spacelike intervals, with channel capacity determined by the condition number of the black hole Smatrix. Furthermore, Grover search can be sped up using the nonunitary dynamics, but polynomialtime solution for exponential search problems implies a 1/polynomial channel capacity for instantaneous signaling. Thus, within this context, we find that the nosignaling principle implies the Grover search lower bound, and allowing exponential small deviations from nosignaling allows only exponentially small improvements to Grover search.
Jul

07/09/15
Adriano Garsia  UCSD
On the Sweep map for Rational Dyck paths
AbstractOur main contribution here is the discovery of a new family of Standard
Tableaux
$
{\cal T}^k_n
$ which are in bijection with the family ${\cal D}_{m,n}$
of Rational Dyck paths for $m=k\times n\pm1$ (the so called ``Fuss'' case). Using this family we
give a new proof of the invertibility of the Sweep map in the Fuss case by
means of a very simple explicit algorithm.This is joint work with Guoce Xin.
Sep

09/18/15
Alessandro Carderi  Technische Universitat Dresden
Full groups of actions of locally compact groups
AbstractThe full group of a probability measure preserving action (of a group) is the group of the measure preserving transformations of the space whose graph is contained in the orbit equivalence relation of the action. For countable groups, these full groups were defined by Dye in '59. He showed that such groups admit a Polish topology and are complete invariant of orbit equivalence. In a joint work with F. Le MaÃ®tre, we extend the notion of full group to probability measure preserving actions of locally compact second countable groups. These full groups also have a Polish topology and they are also complete invariants of orbit equivalence. In this talk, I will define full groups and their topology and I will discuss about some of their topological properties, such as the topological rank.

09/22/15
D. Zaitsev  Trinity College (Dublin)
Convergent normal forms and canonical connections for degenerate real hypersurfaces
AbstractIn their seminal work, S.S. Chern and J. Moser constructed normal forms for realanalytic hypersurfaces with nondegenerate Levi form. More recently, considerable work has been done to construct normal forms in degenerate cases at the level of formal power series. However, apart from that work of ChernMoser, no other cases have been known where the normal form converges. The fundamental obstacle to the convergence being the nonuniformity of the underlying CR geometry.
In a joint work with Ilya Kossovsky, we have constructed such convergent normal forms by constructing canonical connections along natural stratifications of the CR structure.

09/24/15
Howard Barnum  University of New Mexico
Entropy, majorization and thermodynamics in quantum theory and beyond
AbstractGreat progress has recently been made in understanding thermodynamics beyond macroscopic limits by developing quantum thermodynamics as a resource theory, describing what state transitions are possible given specified thermodynamic resources. Thermodynamics has been cited as one of the most robust aspects of physical theory; for example, it has made the transition from classical to quantum. I report preliminary results in an investigation of simple, physically meaningful properties of a physical theory that underly the possibility of such a
thermodynamic resource theory, by studying quantum thermodynamics within the broader realm of "general probabilistic theories". Four such physical properties were shown by Barnum, Mueller, and Ududec to give rise to the finitedimensional quantum framework of density matrices and positive operator valued measures: they are (1) abstract spectrality (2) strong symmetry (3) no higherorder interference and (4) energy observability. I will explain this result and discuss whether or not all four are needed for a reasonable thermodynamics. With a slight strengthening of (1), to unique spectrality, and a significant weakening of (2), to the conjunction of (a) projectivity (an abstraction of certain aspects of the quantum projection postulate (LÂ¸ders' version)) and (b) symmetry of transition probabilities under exchange of states with the unique finegrained effects they make certain, we have the property, important in quantum thermodynamics, that the outcome probabilities for any finegrained measurement are majorized by the spectrum of a state, and hence that measurementprobabilitybased generalizations of classical entropylike functions are given by the classical function applied to the spectrum.This is joint work with Markus Mueller and Cozmin Ududec (characterization of quantum formalism) and with Jonathan Barrett, Marius Krumm, and Markus Mueller (thermodynamics).

09/29/15
Oct

10/01/15
Hanspeter Kraft  University of Basel, Switzerland
Endomorphisms and Automorphisms of Varieties
AbstractJointly with Rafael Andrist we have recently shown that an affine variety $X$ is determined, up to base field automorphisms, by the abstract semigroup of endomorphisms, provided $X$ contains a copy of the affine line.
A more interesting question is how much information about $X$ can be retrieved from the group $Aut(X)$ of automorphisms of $X$. This group has the structure of an indgroup, i.e. an infinite dimensional algebraic group, a concept introduced by Shafarevich in 1966. It was recently studied by several authors, in particular in the case of affine $n$space $A^n$. However, not much is known about this group in general, but there are a number of very interesting examples and conjectures.
In connection with the question above, we can prove the following.
Theorem. If $X$ is a connected affine variety such that $Aut(X)$ is isomorphic to $Aut(A^n)$ as an indgroup, then $X$ is isomorphic to $A^n$ as a variety.
We will explain these concepts and results, and describe some recent development.

10/05/15
Hanspeter Kraft  Universitat Basel
Indvarieties and Indgroups: basic concepts and examples.
AbstractIn 1966 Shafarevich introduced the notion of â€œinfinite dimensional algebraic groupâ€, shortly â€œindgroupâ€. His main application was the automorphism group of affine $nspace \ A^n$ for which he claimed some interesting properties. Recently, jointly with J.Ph. Furter we showed that the automorphism group of any finitely generated (general) algebra has a natural structure of an indgroup, and we further developed the theory.
It turned out that some properties wellknow for algebraic groups carry over to indgroups, but others do not. E.g. every indgroup has a Lie algebra, but the relation between the group and its Lie algebra still remains unclear. As another byproduct of this theory we get new interpretations and a better understanding of some classical results, together with short and transparent proofs.
An interesting â€œtest caseâ€ is $\ Aut(\ A^2)$, the automorphism group of affine 2space, because this group is the amalgamated product of two closed subgroups which implies a number of remarkable properties. E.g. a conjugacy class of an element $g \in \ Aut(\ A^2)$ is closed if and only if $g$ is semisimple, a result wellknown for algebraic groups. A generalization of this to higher dimensions would have very strong and deep consequences, e.g. for the linearization problem.
Note: There will be a $pretalk$ for graduate students from 2:303:00. The speaker has kindly accepted to tell our graduate students what an indgroup is. The regular talk will begin at 3:00.

10/06/15
Peter Oswald  UCSD
Schwarz Iterations: Old and New
AbstractThe name Schwarz iterative methods has been coined in the late 1980ies as a theoretical framework for investigating domain decomposition and multilevel methods for variational problems. They are based on the notion of stable space splittings of a Hilbert space $H$ into a family of auxiliary Hilbert spaces $H_i$, each equipped with its own variational subproblem, and in essence represent a more constructive version of the alternating directions method (ADM) which in turn is a special instance of a POCS algorithm. We consider the multiplicative Schwarz iteration \[ u^{j+1} = u^j + \omega_j w^j_i, \] where finding the update direction $w^j_i$ involves solving the $i$th subproblem, and $\omega_j$ is a relaxation parameter. Which $i=i_j$ is chosen in the $j$th update step matters, until recently only deterministic orderings have been considered.
The renewed interest in investigating random (and greedy) orderings was triggered by results by Strohmer and Vershynin on the convergence of a randomized Kaczmarz method for solving $Ax=b$ (= GaussSeidel with random ordering for $AA^\ast y=b$) which received much attention, both due to the simplicity of the error analysis and the sometimes improved performance. We generalized their result to the setting of Schwarz iterative methods with finitely many subproblems. Even though the a priori bounds for greedy and random orderings are identical, the numerical tests show that the greedy version leads to faster convergence in practice, and that combinations of randomization and greedy approaches can remedy slow convergence of the cheaper randomized iteration. Extensions to infinitely many subproblems are considered. For the case of solving linear systems (SORmethod), some further improvements have recently been made for both deterministic and random orderings.
In the talk, I will briefly review the setup of Schwarz iterative methods and then outline the recently obtained convergence estimates for SORtype methods with deterministic and randomized orderings for linear systems.

10/07/15
Hanspeter Kraft  Universitat Basel
Continuation of lectures on Automorphism Groups of Varieties

10/08/15
Joscha Diehl  Technical University of Berlin and UC San Diego
Weakly asymmetric GinzburgLandau lattice model and stochastic Burgers.
AbstractThe GinzburgLandau lattice model is a system of stochastic differential equations that is known to converge, if properly rescaled, to a linear SPDE. When introducing an asymmetry in the model that vanishes in the limit, we prove convergence to the (semilinear) stochastic Burgers equation. The theory for this stochastic PDE is nontrivial, and we apply the theory of an energy solution. The latter was introduced by GoncalvesJara and under a slight reformulation GubinelliPerkowski were recently able to show wellposedness for this equation.

10/13/15
Miles Jones  UCSD
Pieri Rules for Schur functions in superspace
AbstractThis talk is about recent work with Luc Lapointe of the Universidad de Talca in Chile. I will present what it means to be a Schur function in superspace and what properties they have. One of the first steps to building a theory of symmetric function theory in superspace is to describe the Pieri rules for these superspace versions of Schur functions. In our research, we have
described them and proved that they are correct.Furthermore, we have just started to study the Pieri rules for the Jack polynomials in superspace as a stepping stone to understand the Pieri rules for Macdonald polynomials in superspace. We uncovered a surprise connection to the set of alternating sign matrices and the partition functions of square ice!!!

10/15/15
Eviatar Procaccia  Texas A&M University
The boy who cried Wulff.
AbstractWe consider a Gibbs distribution over random walk paths on the square lattice, proportional to the cardinality of the path's boundary. We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to some norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes.

10/15/15
Justin Roberts  UCSD
TQFT
AbstractThis term I'll give some talks about Topological Quantum Field Theory and related topics in topology, algebra, geometry, physics or whatever. My main plan is not to plan... it's much more fun to digress freely and "do requests" from the audience.

10/15/15
Narutaka Ozawa  Research Institute for Mathematical Sciences (Kyoto)
Noncommutative real algebraic geometry of Kazhdan's property (T)
AbstractKazhdan's property (T) is a representationtheoretic property of groups, which was introduced by Kazhdan in 1967, but has found numerous applications in an amazingly large variety of subjects from representation theory and ergodic theory to combinatorics (expanders) and the theory of networks. I will start with a gentle introduction to the emerging subject of "noncommutative real algebraic geometry," a subject which deals with equations and inequalities in noncommutative
algebra over the reals, with the help of analytic tools such as representation theory and operator algebras. I will then present a surprisingly simple proof that a group $G$ has property (T) if and
only if a certain inequality in the group algebra ${\bf R}[G]$ is satisfied. This inequality is rather amenable to computerassisted analysis and is useful in finding new examples of property (T) groups or better bounds of the Kazhdan constants of known property (T) groups. 
10/19/15
Skip Garibaldi  IPAM
Simple groups stabilizing polynomials
AbstractThe classic Linear Preserver Problem asks to determine, for a polynomial function f on a vector space V, the linear transformations g of V such that fg = f. In case f is invariant under a simple algebraic group G acting irreducibly on V , we note that the subgroup of GL(V) stabilizing f often has identity component G and we give applications realizing various groups, including the largest exceptional group E8, as automorphism groups of polynomials and algebras. We show that starting with a simple group G and an irreducible representation V, one can almost always find an f whose stabilizer has identity component G and that no such f exists in the short list of excluded cases. The main results are new even in the special case where the field is the complex numbers. This talk is about joint work with Bob Guralnick.
Pretalk for Graduate students 2:303:00. 
10/20/15
Alicia Kim  UCSD
Level Set Topology Optimization Method
AbstractThe level set topology optimization method has been drawing attention as a method to integrate conceptual design to manufacturing. The use of level set method has a distinct advantage in naturally handling splitting and merging of boundaries. Topology optimization has been identified as the ideal design method for additive manufacturing and many case studies quote revolutionary weight saving or performance improvement in the order of 20%  80%. My research has been developing the level set topology optimization method for engineering design problems. This seminar will present the existing challenges that will potentially benefit from collaboration with mathematics.

10/22/15
David Renfrew  UCLA
Spectral properties of large NonHermitian Random Matrices.
AbstractThe study of the spectrum of nonHermitian random matrices with independent, identically distributed entries was introduced by Ginibre and Girko. I will present two generalizations of the iid model where the independence and identical distribution assumptions are relaxed.

10/22/15
Justin Roberts  UCSD
TQFT

10/22/15
Isaac Goldbring  University of Illinois, Chicago
Omitting types in C* algebras
AbstractIn typical applications of model theory to various areas of mathematics, deciding which properties are axiomatizable in the sense of firstorder logic is usually key. Thus, when it was first realized that many important properties of C* algebras were not axiomatizable (e.g. nuclearity), it appeared that all hope waslost for an interesting development of the model theory of C* algebras. That pessimism was soon reversed when it was realized that many of these aforementioned properties were socalled â€œomitting typesâ€ properties, which is a specific type of infinitary axiomatizability. Using the Omitting Types Theorem, this has allowed for some interesting results to be proven about C* algebras. I will give a survey of some of the applications of omitting types in C* algebras, including the Kirchberg Embedding Problem, the failure of a finitary version of the Arveson Extension Theorem, and a question of Bankston on the pseudoarc. I will also mention some open questions where the Omitting Types machinery might prove useful, e.g. a problem of Ozawa asking for an example of a nonnuclear C* algebra with both WEP and LLP. I will assume no knowledge of C* algebras or model theory (although some prior knowledge will help in some parts of the talk). Some of the talk will represent joint work with Thomas Sinclair, Martino Lupini, Alessandro Vignati, and Christopher Eagle.

10/26/15
Hans Wenzl  UCSD
Centralizer Algebras for Spinor Representations
AbstractGiven a representation $V$ of a group $G$, it is a classical problem to determine the centralizer of its action on the nth tensor power of $V$. If $V$ is the natural module of a classical Lie group, this led to the famous SchurWeyl and BrauerWeyl dualities.
In this talk, we solve this problem for the spinor representation $S$. For evendimensional Spin groups, the centralizer on the nth tensor power of $S$ is given by a representation of $SO(n)$, with a similar result also for the odddimensional Spin groups. Time permitting, we discuss generalizations of this result to quantum groups and to classification of tensor categories.
Please note: There will be a pretalk for graduate students from 2:30  3:00. The regular talk will begin at 3:00.

10/27/15
Evan Gawlik  UCSD
HighOrder Discretizations of MovingBoundary Problems
AbstractMany important problems in computational science and engineering involve partial differential equations posed on moving domains. This talk will present numerical methods for the solution of such problems, as well as theoretical tools for analyzing their accuracy. I will first introduce a family of highorder finite element methods for movingboundary problems that can handle large domain deformations with ease while representing the geometry of the moving domain exactly. At the core of our approach is the use of a universal mesh: a background mesh that contains the moving domain and conforms to its geometry at all times by perturbing a small number of nodes in a neighborhood of the moving boundary. I will then introduce a unified analytical framework for establishing the convergence properties of a wide class of numerical methods for movingboundary problems. This class includes, as special cases, the technique described above as well as conventional deformingmesh methods (commonly known as arbitrary LagrangianEulerian, or ALE, schemes).

10/28/15
Andrej Zlatos  University of Wisconsin
Growth and singularity in 2D fluids
AbstractThe question of global regularity remains open for many fundamental models of fluid dynamics. In two dimensions, solutions to the incompressible Euler equations have been known to be globally regular since the 1930s, although their derivatives can grow doubleexponentially with time. On the other hand, this question has not yet been resolved for the more singular surface quasigeostrophic (SQG) equation, which is used in atmospheric models. The latter state of affairs is also true for the modified SQG equations, a natural family of PDE which interpolate between these two models.
I will present two results about the patch dynamics version of these equations on the halfplane. The first is globalintime regularity for the Euler patch model, even if the patches initially touch the boundary of the halfplane. The second is localintime regularity for those modified SQG patch equations which are only slightly more singular than Euler, but also existence of their solutions which blow up in finite time. The latter appears to be the first rigorous proof of finite time blowup in this type of fluid dynamics models.

10/29/15
Justin Roberts  UCSD
TQFT

10/29/15
XueMei Li  University of Warwick and MSRI
Limits theorems on Random ODEs on Manifolds and Examples
AbstractWe explain limit theorems associated with a family of random ordinary differential equations on manifolds, driven by randomly perturbed vector fields. After rescaling, the differentiable random curves converge to a Markov process whose Markov generator can be written explicitly in Hormander form. We also give rates of convergence in the Wasserstein distance.
Example 1. A unit speed geodesic, which chooses a direction randomly and uniformly at every instant of order $1\epsilon$, converges to a Brownian motion as epsilon tends to 0. Furthermore their horizontal lifts converge to the Horizontal Brownian motion.
Examples 2. Inspired by the problem of the convergence of Berger's spheres to a $S ^ {1/2}$, we introduce a family of Interpolation equations on a Lie group $G$. These are stochastic differential equations on a Lie group driven by diffusion vector fields in the direction of a subgroup $H$ rescaled by $1\epsilon$, and a drift vector field in a transversal direction. If there is a reductive structure, we identify a family of slow variables which, after rescaling, converges to a Markov process on $G$. Furthermore, the projection of the limiting Markov process to the orbit manifolds $G/H$ is Markov. The limits can be identified in terms of the eigenvalue of a second order differential operator on the subgroup and the $Ad(H)$ invariant decomposition of the Lie algebra.

10/29/15
Ludmil Zikatanov  Penn State University
Stability and monotonicity in the low order discretizations of Biot's model of poroelasticity
AbstractWe consider a finite element discretizations of the Biot's model in poroelasticity with lowest order (MINI and stabilized P1P1) elements. We show convergence of discrete schemes which are implicit in time and use these types of elements in space. We also address the issue related to the presence of nonphysical oscillations in the pressure approximations for low permeabilities and/or small time steps and present numerical results confirming the monotone behavior of two stabilized schemes. This is a joint work with Carmen Rodrigo, Francisco Gaspar (Univ. Zaragoza) and Xiaozhe Hu (Tufts).

10/29/15
Martin Hairer  Fields Medalist, Regius Professor of Mathematics at University of Warwick
Taming Infinities
AbstractSome physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! Various techniques, usually going under the common name of â€œrenormalisationâ€ have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will tip our toes into some of the mathematical aspects of these techniques and we will see how they have recently been used to make precise analytical statements about the solutions of some equations whose meaning was not even clear until now.
Nov

11/02/15
Giovanni Motta  Columbia University
Locally Stationary Latent Factors
AbstractOur approach for fitting dynamic nonstationary factor models to multivariate time series is based
on the principal components of the estimated timevarying spectraldensity matrix. This approach
allows the spectral matrix to be smoothly timevarying, which imposes very little structure on the
moments of the underlying process. However, the estimation delivers timevarying filters that are
highdimensional and twosided. Moreover, the estimation of the spectral matrix strongly depends
on the chosen bandwidths for smoothing over frequency and time. As an alternative, we propose a
new semiparametric approach in which only part of the model is allowed to be timevarying. More
precisely, the latent factors admit a dynamic representation with timevarying autoregressive
coefficients while the loadings are constant over time. Estimation of the model parameters is
accomplished by application of the EM algorithm and the Kalman filter. The timevarying parameters are modeled locally by polynomials and estimated by maximizing the likelihood locally. Compared to estimation of the factors by principal components, our new approach produces superior results in particular for small crosssectional dimension. 
11/02/15
Brian Longo  UCSD
Superapproximation for linear groups in positive characteristic.
AbstractLet $\Omega\subseteq {\rm GL}_n(F_p(t))$ be a finite symmetric set containing the identity. Let $\Gamma$ be the group generated by $\Omega$ and let $\mathbb{G}$ be the Zariskiclosure of $\Gamma$. We discuss conditions on which the family of Cayley graphs $\{{\rm Cay}(\Gamma ({\rm mod} Q), \Omega)\}$ is a family of Cayley graphs as $Q$ ranges through a certain subset $\Sigma$ of $F_p[t]$. This problem is a positive characteristic variation of the work of BourgainGamburd, Varju, Salehi GolsefidyVarju, and others. We focus on the difficulties that arise in positive characteristic.
Please note: There will be pretalk for graduate students from 2:30  3:00. The regular talk will begin at 3:00.

11/03/15
Chris Deotte  UCSD
Domain Partitioning Methods for Elliptic Partial Differential Equations
AbstractNumerically solving elliptic partial differential equations for a large number of degrees of freedom requires the parallel use of many computer processors. This in turn requires algorithms to partition domains into subdomains in order to distribute the work.
In this talk, we present five novel algorithms for partitioning domains that utilize information from the underlying PDE. When a PDE has strong convection or anisotropic diffusion, directional dependence exists and a partition that favors this direction is desirable. Our schemes fall into two classes; one class creates rectangular shaped subdomains aligned in this direction and one class creates subdomains that increase in size as you move in this direction.These schemes are mathematically described and analyzed in detail. Then they are tested on a variety of experiments which include solving the convectiondiffusion equation for 1/4 billion unknowns on 512 processors using over 1 teraflop of computing power.
Theory and experiments demonstrate that these schemes improve the domain decomposition convergence rate when the underlying PDE has directional dependence. In our hundreds of experiments, the number of DD iterations required for convergence reduces by a factor between 0.25 and 0.75. And these methods maintain or improve the final finite element solution's accuracy also.

11/03/15
Kenneth Barrese  UCSD
p,q analogues of mlevel rook numbers
AbstractThis talk presents joint work with Nicholas Loehr, Jeffrey Remmel, and Bruce Sagan. The mlevel rook placements are a generalization of ordinary rook placements. By factoring the mlevel rook polynomials of Ferrers boards, it is possible to partition them into equivalence classes.
There is a p,qanalogue of the mlevel rook numbers. We have a bijective proof that two boards with the same mlevel rook numbers have the same qanalogues of their mlevel rook numbers. Surprisingly, they may not have the same panalogues.

11/05/15
Yusuke Isono  RIMS (Kyoto) and UCLA
Biexact groups, strongly ergodic actions and group measure space type III factors with no central sequence
AbstractWe investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras arising from arbitrary actions of biexact discrete groups (e.g. free groups) on amenable von Neumann algebras. We particularly prove a spectral gap rigidity result for the crossed products and, using recent results of BoutonnetIoanaSalehi Golsefidy, we provide the first example of group measure space type III factors with no central sequences. This is joint work with C. Houdayer.

11/05/15
Justin Roberts  UCSD
TQFT

11/05/15
Steven Heilman  UCLA
Low Correlation Noise Stability of Euclidean Sets
AbstractThe noise stability of a Euclidean set is a wellstudied quantity. This quantity uses the OrnsteinUhlenbeck semigroup to generalize the Gaussian perimeter of a set. The noise stability of a set is large if two correlated Gaussian random vectors have a large probability of both being in the set. We will first survey old and new results for maximizing the noise stability of a set of fixed Gaussian measure. We will then discuss some recent results for maximizing the lowcorrelation noise stability of three sets of fixed Gaussian measures which partition Euclidean space. Finally, we discuss more recent results for maximizing the lowcorrelation noise stability of symmetric subsets of Euclidean space of fixed Gaussian measure. All of these problems are motivated by applications to theoretical computer science.

11/05/15
Jinchao Xu  Penn State University
An Integrated Study of Modeling, Discretization and Preconditioning for Magnetohydrodynamics
AbstractI will report some recent works on structurepreserving and stable discretization of magnetohydrodynamics and robust preconditioning methods for the resulting algebraic systems. In particular, judging from theoretical and/or numerical analysis of several mathematical models for magnetohydrodynamics (MHD) which involve the coupling of NavierStokes with Maxwell equations, I will argue that some more complicated models may be easier to simulate than some simplified models that have been often used in practice.

11/09/15
Robert Won  UCSD
Zgraded noncommutative projective geometry
AbstractThe first Weyl algebra $A = k\langle x, y \rangle/(xy  yx  1)$ is $\mathbb{Z}$graded with deg x = 1 and deg y = 1. Susan Sierra and Paul Smith studied the category of graded modules over A, showing that this category was equivalent to coherent sheaves on a certain quotient stack. In this talk, we investigate the graded module categories over $\mathbb{Z}$graded rings called generalized Weyl algebras. We construct commutative rings with equivalent graded module categories. In the pretalk, we will discuss some preliminaries on categories and graded rings before giving an overview of noncommutative projective geometry.
Please note: There will be a pretalk for graduate students from 2:30  3:00. The regular talk will begin at 3:00.

11/09/15
Erik Carlsson  Harvard University, Center of Mathematical Sciences and Applications
A proof of the shuffle conjecture
AbstractRecently, Anton Mellit and I gave a proof of the famous shuffle conjecture of Haglund, Haiman, Loehr, Ulyanov, and Remmel, which predicts a combinatorial formula for the character of the diagonal coinvariant algebra, and other quantities in algebraic geometry. I'll explain what this conjecture is about, and explain the algebraic structures that go into this recent proof. Hopefully if there's time, I'll explain some of remarkable unsolved generalizations, and their role in algebraic geometry.

11/10/15
Erik Carlsson  Harvard University, Center of Mathematical Sciences and Applications
Character formulas from switching limits
AbstractGraeme Segal once conjectured that there should be a proof of the Kac character formula for affine KacMoody algebras using equivariant localization on the affine Grassmannian, analogous to the famous example done by Atiyah and Bott for the Weylcharacter formula using BorelWeilBott. He noticed that the idea formally gives the desired answer, modulo several technical considerations such as the infinite dimensionality of the space, singularities, and vanishing of higher Cech cohomology groups. I'll explain how these formulas in type A follow provided one is able to switch two limits in the equivariant Ktheory of the infinite dimensional Grassmannian variety into which the affine Grassmannian imbeds. I'll explain a theorem of mine that says gives sufficient (and possibly necessary) conditions in the form of some subtle inequalities for when the limit switching holds, and explain some other examples from Macdonald theory that follow such as the famous constant term formula in type A. I'll then explain the value in studying this question for other varieties, perhaps associated to other root systems.

11/12/15
Justin Roberts  UCSD
TQFT

11/12/15
Lionel Levine  Cornell University
Threshold state of the abelian sandpile
AbstractA sandpile on a graph is an integervalued function on the vertices. It evolves according to local moves called topplings. Some sandpiles stabilize after a finite number of topplings, while others topple forever. For any sandpile $s_0$ if we repeatedly add a grain of sand at an independent random vertex, we eventually reach a "threshold state'' $s_T$ that topples forever. Poghosyan, Poghosyan, Priezzhev and Ruelle conjectured a precise value for the expected amount of sand in $s_T$ in the limit as $s_0$ tends to negative infinity. I will outline how this conjecture was proved by means of a Markov renewal theorem.

11/12/15
Karola Meszaros  Cornell University
Realizing subword complexes via triangulations of root polytopes
AbstractSubword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. We show that a family of subword complexes can be realized geometrically via triangulations of root polytopes. This implies that a family of $beta$Grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. Based on joint work with Laura Escobar.

11/12/15
Alex Furman  UIC
Superrigidity  from arithmeticity to actions on manifolds
AbstractA remarkable phenomenon discovered by G.A.Margulis in the 1970s, now called superrigidity,
concerns linear representations of discrete subgroups groups in such groups as SL(3,R).
As one of the applications of superrigidity Margulis proved arithmeticity of these groups. In the 1980s R.J.Zimmer extended Margulis' work to the context of cocycles, that found many applications in Ergodic Theory and Geometry of actions on manifolds. In the talk I plan to give a broad overview of some of these topics and discuss some recent developments. 
11/17/15
Antonio Palacios  San Diego State University
Complex Networks: Connecting Equivariant Bifurcation Theory with Engineering Applications
AbstractThe advent of novel engineered or smart materials, whose properties can be significantly altered in a controlled fashion by external stimuli, has stimulated the design and fabrication of smaller, faster, and more energyefficient devices. As the need for even more powerful technologies grows, networks have become popular alternatives to advance the fundamental limits of performance of individual devices. Thus, in the first part of this talk we provide an overview of fifteen years of work aimed at combining ideas and methods from equivariant bifurcation theory to model, analyze and fabricate novel technologies such as: ultrasensitive magnetic and electric field sensors; networks of nano oscillators; and multifrequency converters.
In the second part of the talk, we discuss more recent work on networks of vibratory gyroscopes systems. Under normal conditions of operation, the model equations can be reformulated in a Hamiltonian structure and the corresponding normal forms are then derived. Through a normal form analysis, we investigate the effects of various coupling topologies and unravel the nature of the bifurcations that lead a ring of gyroscopes of any size into and out of synchronization. The synchronization state is particularly important because it can lead to a significant reduction in phase drift, thus enhancing performance. The Hamiltonian approach can, in principle, be readily extended to other symmetry related systems.

11/17/15
Gordon Heier  University of Houston
Holomorphic sectional curvature and the structure of projective Kaehler manifolds
AbstractI will present recent results on the consequences of semidefinite holomorphic sectional curvature for the geometric structure of projective Kaehler manifolds. In the semipositive case, the focus is on the existence of rational curves. In the seminegative case, the focus is on semipositivity of the canonical line bundle and splitting theorems. This talk covers various joint works with S. Lu, B. Wong and F. Zheng.

11/17/15
Daniel Drimbe  UCSD
Cocycle superrigidity for coinduced actions
AbstractPopa's deformation/rigidity theory led to a remarkable cocycle superrigidity theorem for Bernoulli actions of groups with property (T) (2005) and of products of nonamenable groups (2006). More precisely, Popa obtained that every cocycle for such an action with values in a countable (and more generally, in a $\mathcal U_{fin}$) group is cohomologous with a group homomorphism. In this talk, we will present a generalization of this theorem to coinduced actions.

11/17/15
Gang Liu  UC Berkeley
On the uniformization conjecture of Yau and related problems
AbstractThe uniformization theorem in one complex variable states that a simply connected Riemann surface is either isomorphic to the Riemann sphere, the Poincare disk, or the complex plane. The uniformization conjecture, proposed by Yau in 1974, looks for possible generalizations in higher dimensions. The conjecture states that a complete noncompact Kahler manifold with positive bisectional curvature is biholomorphic to the complex Euclidean space. In this talk, I will discuss some recent progress on this conjecture and related problems.

11/19/15
Joseph Palmer  UCSD
Symplectic Gcapacities and integrable systems

11/23/15
Joseph Palmer  UCSD
Classifying toric and semitoric fans by lifting equations from $SL(2,\mathbb{Z})$
AbstractWe present an algebraic method to study fourdimensional toric varieties by lifting matrix equations from the special linear group $SL(2,\mathbb{Z})$ to its preimage in the universal cover of $SL(2,\mathbb{R})$. With this method we recover the classification of two dimensional toric fans, and obtain a description of their semitoric analogue. As an application to symplectic geometry of Hamiltonian systems, we give a concise proof of the connectivity of the moduli space of toric integrable systems in dimension four, recovering a known result, and extend it to the case of semitoric integrable systems with a fixed number of focusfocus points. (joint work with Daniel Kane and Alvaro Pelayo)
Please note: There will be a pretalk for graduate students from 2:30  3:00. The regular talk will begin at 3:00.

11/24/15
John Moody  UCSD
Finite Element Regularity on Combinatorial Manifolds without Boundary
AbstractThe Finite Element Method in its most simple form considers piecewise polynomials on a triangulated space $\Omega$. While the general theory does not require structure on $\Omega$ beyond admitting a finite triangulation, it is quickly realized that in order to solve partial differential equations, $\Omega$ must be endowed with a differentiable structure. We introduce a new framework which has the potential to allow the Finite Element Method access to a broad class of differentiable manifolds of nontrivial topology.

11/24/15
RenCang Li  University of Texas, Arlington
A Krylov Subspace Method for LargeScale SecondOrder Cone Linear Complementarity Problem
AbstractOptimization problems with second order cone constraints have wide range of applications in engineering, control, and management science. In this talk, we present an efficient method based on Krylov subspace approximation for solving the second order cone linear complementarity problem (SOCLCP). Here, we first show that SOCLCP can be solved by finding a positive zero $s_*\in \mathbb{R}$ of a particular rational function $h(s)$, and then propose a Krylov subspace method to reduce $h(s)$ to $h_{\ell}(s)$ as in the model reduction. The zero $s_*$ of $h(s)$ can be accurately approximated by that of $h_{\ell}(s)=0$ which itself can be casted as a small eigenvalue problem. The new method is made possible by our complete description of the curve $h(s)$, and it is suitable for large scale problems. The new method is tested and compared against the bisection method recently proposed and two other stateoftheart packages: SDPT3 and SeDuMi. Our numerical results show that the method is very efficient both for smalltomedium dense problems as well as for large scale problems.
This is a joint work with LeiHong Zhang (Shanghai University of Finance and Economics),
Wei Hong Yang (Fudan University), and Chungen Shen (Shanghai Finance University). 
11/30/15
D.A.S. Fraser  University of Toronto
On combining likelihoods, pvalues, or scores: From many small dependent inputs to valid global inference
AbstractWith larger data sizes and often unobservable variables, statistical models have become progressively larger and structurally complex and even computationally intractable. In applications, workarounds have arisen that add say loglikelihoods and adjust for breakdown in Bartlett relations, but usually with the loss of first order accuracy. Meanwhile, likelihood asymptotics has sought progressively higher accuracy for pvalue functions and now provides definitive thirdorder pvalues and related likelihood functions. We apply the likelihood asymptotic approach to this combining problem and are able to convert composite likelihood to a fully firstorder accurate procedure. The methods can then be extended to the combining of statistically dependent pvalues and scores.

11/30/15
Jeremy Semko  UCSD
Controlled Rough Paths on Manifolds

11/30/15
Robert Guralnick  USC
Base size, stabilizers and generic stabilizers for simple algebraic groups.
AbstractLet G be a group acting (faithfully) on a set X. A base for this action is a subset Y of X so that no element of G fixes every element of Y. The question of what is the minimal size of a base is a classical subject going back to the early days of finite permutation group theory.
In this talk I will mostly focus on the case that G is simple algebraic group and X is an irreducible variety. A closely related problem is to determine a generic stabilizer (if it exists). Note that base size 1 is the same as saying some stabilizer is trivial (and indeed base size b on X is the same as saying base size 1 on b copies of X).
We will consider the case where X = G/H for some maximal closed subgroup H and for the case that X is an irreducible rational Gmodule. Even if one is only interested in the case of finite groups, these cases are relevant.
Some of this is joint work with Burness and Saxl, some with Lawther and some with Garibaldi.
Please note: There will be a pretalk for graduate students from 2:30  3:00. The regular talk will begin at 3:00.
Dec

12/03/15
Justin Roberts  UCSD
TQFT

12/03/15
Romyar Sharifi  University of Arizona
Unramified Iwasawa modules
AbstractIwasawa theory concerns the growth of arithmetic objects in towers of number fields. The unramified Iwasawa modules that are the inverse limits of pparts of class groups up such a tower are central objects in the study of Iwasawa theory. I will discuss a variety of conjectures and results on the structure of unramified Iwasawa modules, along with applications. In particular, I intend to explain Iwasawatheoretic refinements of Leopoldt's reflection principle which form part of joint work with Bleher, Chinburg, Greenberg, Kakde, Pappas, and Taylor.

12/03/15
Herbert Heyer  University of Tuebingen
The Liouville property of harmonic functions related to a random walk in a group
AbstractThe classical Liouville property asserts that bounded harmonic functions on Euclidean space are necessarily constant. This property has been extended to $\mu$harmonic functions related to a random walk $S$ in a locally compact group $G$ with defining measure $\mu$. In the present talk the dependence on $G$ and $\mu$, of the asymptotic entropy $h(G,\mu)$ of $S$, will be studied. The case $h(G,\mu)=0$ characterizes the Liouville property, and $h(G,\mu)>0$ leads to the wellknown boundary theory of H. Furstenberg.

12/03/15
Romyar Sharifi  University of Arizona
Modular symbols and arithmetic
AbstractIn 1844, Kummer showed that cyclotomic integer rings can fail to be principal ideal domains. In 1976 and 1984, Ribet and MazurWiles used Galois representations attached to modular forms to partially describe class groups that measure the extent of this failure. The exact structure of these class groups remains a mystery to this day. I will explain how to attach ideal classes to geodesics in the complex upper halfplane. A conjecture of mine states these two constructions are inverse to each other in an appropriate sense. I hope to motivate a broader philosophy, developed jointly with Takako Fukaya and Kazuya Kato, that certain arithmetic objects attached to Galois representations of global fields can be described using higherdimensional modular symbols.

12/04/15
Tianyi Zheng  Stanford University
Random walk parameters and the geometry of groups
AbstractThe first characterization of groups by an asymptotic description of random walks on their Cayley graphs dates back to Kestenâ€™s criterion of amenability. I will first review some connections between the random walk parameters and the geometry of the underlying groups. I will then discuss a flexible construction that gives solution to the inverse problem (given a function, find a corresponding group) for large classes of speed, entropy and return probability of simple random walks on groups of exponential volume growth. Based on joint work with Jeremie Brieussel.

12/08/15
Daniel Remenik  Universidad de Chile
Nonintersecting Brownian motions and random matrices
AbstractThe KardarParisiZhang (KPZ) universality class is a broad collection of probabilistic models including stochastic PDEs, random growth models and directed polymers. Models in this class show unusual, nonGaussian fluctuations, which for some special classes of initial data are described by objects coming from random matrix theory (RMT). While the connection between KPZ and RMT is well understood in the case of curved initial data, the case of flat initial data has remained a bit of a mystery.
After introducing these topics, I will present a result about a system of $N$ Brownian motions conditioned not to intersect on a finite time interval. The result shows that the distribution of the squared maximal height of the top path in this system coincides with that of the largest eigenvalue of a certain (finite) random matrix, known as a real Wishart or LOE matrix. I will describe how this result provides an explanation for the connection between KPZ and RMT in the flat case, and how it generalizes some older results concerning its $N \to \infty$ scaling limit. Based on joint work with Gia Bao Nguyen.

12/08/15
Quang Bach  UCSD
Fibonacci analogues of the Stirling numbers and the Lah numbers.
AbstractWe define Fibonacci analogues of the Stirling numbers of the first and second kind and the Lah numbers. We will describe a new rook theory model which allows us to give combinatorial
interpretations the Fibonacci analogues the Stirling numbers of the first and second kind and the Lah numbers as well as certain $q$analogues and $p,q$analogues of such numbers. 
12/10/15
Justin Roberts  UCSD
TQFT

12/10/15
Mary Wootters  Carnegie Mellon University
From compressed sensing to coding theory
AbstractI'll discuss two problems, which on the surface seem quite different. The first, which comes up in signal processing and in algorithm design, is the problem of coming up with linear, geometrypreserving maps which are efficient to store and manipulate. The second, which comes up in coding theory and theoretical computer science, is the problem of establishing the listdecodability  a combinatorial property  of error correcting codes. I'll establish a connection between these two problems, and discuss how techniques from highdimensional probability can be used to handle both. Punchlines include improved fast JohnsonLindenstrauss transforms and structured RIP matrices, and the answer to some longstanding combinatorial open questions in coding theory.

12/15/15
Nathan Williams  Laboratoire de Combinatoire et d'Informatique Math\`ematique (LaCIM) Universit\'e du Qu\'ebec \`a Montr\'eal
Sweeping Up Zeta
AbstractUsing techniques introduced by H. Thomas and N. Williams in "Cyclic Symmetry of the Scaled Simplex," we prove that modular sweep maps are bijective. We conclude that the general sweep maps defined by D. Armstrong, N. Loehr, and G. Warrington in "Sweep Maps: A Continuous Family of Sorting Algorithms" are bijective. As a special case, this proves that the zeta map on rational Dyck paths is a bijection.