Tue, Jan 25 2022
MCMC vs. variational inference -- for credible learning and decision making at scale

Center for Computational Mathematics Seminar

Zoom ID 922 9012 0877

I will introduce some recent progress towards understanding the scalability of Markov chain Monte Carlo (MCMC) methods and their comparative advantage with respect to variational inference. I will discuss an optimization perspective on the infinite dimensional probability space, where MCMC leverages stochastic sample paths while variational inference projects the probabilities onto a finite dimensional parameter space. Three ingredients will be the focus of this discussion: non-convexity, acceleration, and stochasticity. This line of work is motivated by epidemic prediction, where we need uncertainty quantification for credible predictions and informed decision making with complex models and evolving data.

Towards Splitting $BP \langle 2 \rangle \wedge BP\langle 2 \rangle$ at Odd Primes

Math 292 - Topology seminar

In the 1980s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of $bo \wedge bo$ and $l \wedge l$.These splittings helped make it feasible to do computations using the $bo$- and $l$-based Adams spectral sequences.I will discuss progress towards an analogous splitting for $BP\langle 2 \rangle \wedge BP \langle 2 \rangle$ at odd primes.

Morava's orbit picture and Morava stabilizer groups

Math 292 - Topology seminar (student talk series on chromatic homotopy theory)

Min-max Theory for Capillary Surfaces

Department Colloquium

Zoom ID:   964 0147 5112

Capillary surfaces model interfaces between incompressible immiscible fluids. The Euler-Lagrange equations for the capillary energy functional reveals that such surfaces are solutions of the prescribed mean curvature equation, with prescribed contact angle where the interface meets the container of the fluids. Min-max methods have been used with great success to construct unstable critical points of various energy functionals, particularly for the special case of closed minimal surfaces. We will discuss the development of min-max methods to construct general capillary surfaces.

Thu, Jan 27 2022
The lower bound of the integrated Carath Ìeodory-Reiffen metric and Invariant metrics on complete noncompact Kaehler manifolds

Math 258 - Seminar in Differential Geometry

AP&M Room 7321
Zoom ID: 949 1413 1783

We seek to gain progress on the following long-standing conjectures in hyperbolic complex geometry: prove that a simply connected complete K Ìˆahler manifold with negatively pinched sectional curvature is biholomorphic to a bounded domain and the Carath Ìeodory-Reiffen metric does not vanish everywhere. As the next development of the important recent results of D. Wu and S.T. Yau in obtaining uniformly equivalence of the base K Ìˆahler metric with the Bergman metric, the Kobayashi-Royden metric, and the complete Ka Ìˆhler-Einstein metric in the conjecture class but missing of the Carath Ìeodory-Reiffen metric, we provide an integrated gradient estimate of the bounded holomorphic function which becomes a quantitative lower bound of the integrated Carath Ìeodory-Reiffen metric. Also, without requiring the negatively pinched holomorphic sectional curvature condition of the Bergman metric, we establish the equivalence of the Bergman metric, the Kobayashi-Royden metric, and the complete Ka Ìˆhler-Einstein metric of negative scalar curvature under a bounded curvature condition of the Bergman metric on an n-dimensional complete noncompact Ka Ìˆhler manifold with some reasonable conditions which also imply non-vanishing Carath Ìedoroy-Reiffen metric. This is a joint work with Kyu-Hwan Lee.

The Infinite Conjugacy Class Property and its Applications in Random Walks and Dynamics

Department Colloquium

Zoom ID:   964 0147 5112

A group is said to have the infinite conjugacy class (ICC) property if every non-identity element has an infinite conjugacy class. In this talk I will survey some ideas in geometric group theory, harmonic functions on groups, and topological dynamics and show how the ICC property sheds light on these three seemingly distinct areas. In particular I will discuss when a group has only constant bounded harmonic functions, when every proximal dynamical system has a fixed point, and what this all has to do with the growth of a group. No prior knowledge of harmonic functions on groups or Topological dynamics will be assumed.

This talk will include joint work with Anna Erschler, Yair Hartman, Omer Tamuz, and Pooya Vahidi Ferdowsi.

Normal approximation for traces of random unitary matrices

Math 288 - Probability and Statistics

For zoom ID and password email: ynemish@ucsd.edu

Self-simulable groups

Math 211B - Group Actions Seminar

Zoom ID 967 4109 3409
Email an organizer for the password

We say that a finitely generated group is self-simulable if every action of the group on a zero-dimensional space which is effectively closed (this means it can be described by a Turing machine in a specific way) is the topological factor of a subshift of finite type on said group. Even though this seems like a property which is very hard to satisfy, we will show that these groups do exist and that their class is stable under commensurability and quasi-isometries of finitely presented groups. We shall present several examples of well-known groups which are self-simulable, such as Thompson's V and higher-dimensional general linear groups. We shall also show that Thompson's group F satisfies the property if and only if it is non-amenable, therefore giving a computability characterization of this well-known open problem. Joint work with Mathieu Sablik and Ville Salo.

Absolutely Robust Control Modules in Chemical Reaction Networks

Math 218 - Seminars on Mathematics for Complex Biological Systems

Contact Bo Li at bli@math.ucsd.edu for the Zoom info

We use ideas from the theory of absolute concentration robustness to control a species of interest in a given chemical reaction network. The results are based on the network topology and the deficiency of the system, independent of reaction parameter values. The control holds in the stochastic regime and the quasistationary distribution of the controlled species is shown to be approximately Poisson under a specific scaling limit.

https://mathweb.ucsd.edu/~bli/research/mathbiosci/MBBseminar/

Howe Duality for Exceptional Theta Correspondences

Math 209 - Number Theory Seminar

Pre-talk at 1:20 PM

APM 6402 and Zoom;
See https://www.math.ucsd.edu/~nts/

The theory of local theta correspondence is built up from two main ingredients: a reductive dual pair inside a symplectic group, and a Weil representation of its metaplectic cover. Exceptional correspondences arise similarly: dual pairs inside exceptional groups can be constructed using so-called Freudenthal Jordan algebras, while the minimal representation provides a suitable replacement for the Weil representation. The talk will begin by recalling these constructions. Focusing on a particular dual pair, we will explain how one obtains Howe duality for the correspondence in question. Finally, we will discuss applications of these results. The new work in this talk is joint with Gordan Savin.

Fri, Jan 28 2022
Double nested Hilbert schemes and stable pair invariants

Math 208 - Algebraic Geometry Seminar

Pre-talk at 10:00 AM

Contact Samir Canning (srcannin@ucsd.edu) for zoom access.

Hilbert schemes of points on a smooth projective curve are simply symmetric powers of the curve itself; they are smooth and we know essentially everything about them. We propose a variation by studying double nested Hilbert schemes of points, which parametrize flags of 0-dimensional subschemes satisfying certain nesting conditions dictated by Young diagrams. These moduli spaces are almost never smooth but admit a virtual structure à la Behrend-Fantechi. We explain how this virtual structure plays a key role in (re)proving the correspondence between Gromov-Witten invariants and stable pair invariants for local curves, and say something on their K-theoretic refinement.

Tue, Feb 1 2022
Ranks of linear pencils separate similarity orbits of matrix tuples

Math 243 - Functional Analysis Seminar

Please email djekel@ucsd.edu for Zoom details

The talk addresses the conjecture of Hadwin and Larson on joint similarity of matrix tuples, which arose in multivariate operator theory.

The main result states that the ranks of linear matrix pencils constitute a collection of separating invariants for joint similarity of matrix tuples, which affirmatively answers the two-sided version of the said conjecture. That is, m-tuples X and Y of n×n matrices are simultaneously similar if and only if rk L(X) = rk L(Y) for all linear matrix pencils L of size mn. Similar results hold for certain other group actions on matrix tuples. On the other hand, a pair of matrix tuples X and Y is given such that rk L(X) <= rk L(Y) for all L, but X does not lie in the closure of the joint similarity orbit of Y; this constitutes a counter-example to the general Hadwin-Larson conjecture.

The talk is based on joint work with Harm Derksen, Igor Klep and Visu Makam.