Fri, Feb 3 2023
##### How the lizard got its colors

Special Theoretical Biophysics Seminar

Mayer Room, 4322 Mayer Hall

How a Turing's reaction-diffusion process in a biological context leads to a rather surprising appearance of Ising-like colorings of the skin of Mediterranean lizards.

Mon, Feb 6 2023
##### A twisted approach to the Balmer spectrum of the stable module category of a Hopf algebra

Seminar in Algebra-Math 211A

APM 7321

The Balmer spectrum of a tensor triangulated category is a topological tool analogous to the usual spectrum of a commutative ring. It provides a universal theory of support, giving a categorical framework to (among others) the support varieties that have been used to great effect in modular representation theory. In this talk I will present an approach to the Balmer spectrum of the stable module category of a Hopf algebra using twisted tensor products and emphasizing examples. This will include an unpretentious introduction to twisted tensor products, the Balmer spectrum, and the relevance of both in representation theory.

Tue, Feb 7 2023
##### Variational Analysis of some nonlocal functionals and associated function spaces

MATH 248 - Seminar In Real Analysis

APM 7321

I will present a recent work on variational problems involving nonlocal energy functionals that appear in nonlocal mechanics. The well-posedness of variational problems is established via a careful study of the associated energy spaces, which are nonstandard. I will discuss some difficulties in proving fundamental structural properties of the function spaces such as compactness. For a sequence of parametrized nonlocal functionals in suitable form, we compute their variational limit and establish a rigorous connection with classical models.

##### Wave Simulations in Infinite Spacetime

Computational Geometric Mechanics Research Seminar

APM 7321

The development of accurate and efficient numerical solutions to the wave equation is a fundamental area of scientific research with applications in several fields, including music, computer graphics, architecture, and telecommunications. A key challenge in wave simulation research concerns the proper handling of wave propagation on an unbounded domain. This challenge is known as the infinite domain problem. In this talk, I present a novel geometric framework for solving this problem based on the classical Kelvin transformation. I express the wave equation as a Laplace problem in Minkowski spacetime and show that the problem is conformally invariant under Kelvin transformations using the Minkowski metric while the boundedness of the spacetime is not. These two properties of the Kelvin transformation in Minkowski spacetime ensure that harmonic functions which span infinite spacetime can be simulated using finite computational resources with no loss of accuracy.

##### Configuration spaces and combinatorial algebras

Combinatorics Seminar (Math 269)

APM 7321

In this talk, I will discuss connections between configuration spaces, an important class of topological space, and combinatorial algebras arising from the theory of reflection groups. In particular, I will present work relating the cohomology rings of some classical configuration spaces - such as the space of n ordered points in Euclidean space - with Solomon descent algebra and the peak algebra. The talk will be centered around two questions. First, how are these objects related? Second, how can studying one inform the other? This is joint, on-going work with Marcelo Aguiar and Vic Reiner.

Wed, Feb 8 2023
##### Games for Couples

Food for Thought

HSS 4025

In this talk, I will introduce a few games for you and your partner (if any exists) to play. They can help you get to know each other and descriptive set theory better. It’s all fun and games.

##### Nonlinear PDEs - A Journey

Math 296 - Graduate Student Colloquium

APM 7321

This talk will provide a basic introduction to the world of nonlinear PDEs.

Thu, Feb 9 2023
##### Compact URS and compact IRS

Math 211B - Group Actions Seminar

APM 7218 and Zoom ID 967 4109 3409
Email an organizer for the password

I will discuss compact uniformly recurrent subgroups and compact invariant random subgroups in locally compact groups, and present results from ongoing projects with Pierre-Emanuel Caprace and Waltraud Lederle, and with Tal Cohen.

##### Min-max construction of anisotropic CMC surfaces

Math 258-Differential Geometry

APM 7321

We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard [Invent. Math.,1983] in dimension 3.

##### Scaling limits for non-Markovian epidemic models in large populations

Stochastic Systems Seminar, Math 288D

Via zoom (please email Professor Williams for Zoom information)

In this talk we will discuss several stochastic epidemic models recently developed to account for general infectious durations, infection-age dependent infectivity and/or progress loss of immunity/varying susceptibility, extending the standard epidemic models. We construct individual based stochastic models, and prove scaling limits for the associated epidemic dynamics in large populations. Each individual is associated with a random function/process that represents the infection-age dependent infectivity force to exert on other individuals. We extend this formulation to associate each individual with a random function that represents the loss of immunity/varying susceptibility. A typical infectivity function first increases and then decreases from the epoch of becoming infected to the time of recovery, while a typical immunity/susceptibility function gradually increases from the time of recovery to the time of losing immunity and becoming susceptible. The scaling limits are deterministic and stochastic Volterra integral equations. We also discuss some new PDEs models arising from the scaling limits. (This talk is based on joint work with Etienne Pardoux, Raphael Forien, and Arsene Brice Zosta Ngoufack.)

##### Large values of eigenfunctions on hyperbolic manifolds

Math 209: Number Theory Seminar

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

It is a folklore conjecture that the sup norm of a Laplace eigenfunction on a compact hyperbolic surface grows more slowly than any positive power of the eigenvalue.  In dimensions three and higher, this was shown to be false by Iwaniec-Sarnak and Donnelly.  I will present joint work with Farrell Brumley that strengthens these results, and extends them to locally symmetric spaces associated to $\mathrm{SO}(p,q)$.

[pre-talk at 1:20PM]

Thu, Feb 23 2023
##### Robust sublinear expanders

Department Colloquium

APM 6402

Expander graphs are perhaps one of the most widely useful classes of graphs ever considered. In this talk, we will focus on a fairly weak notion of expanders called sublinear expanders, first introduced by Komlós and Szemerédi around 25 years ago. They have found many remarkable applications ever since. In particular, we will focus on certain robustness conditions one may impose on sublinear expanders and some applications of this very recent idea, which include:

- recent progress on one of the most classical decomposition conjectures in combinatorics, the Erdős-Gallai Conjecture,

- Rainbow Turan problem for cycles, raised by Keevash, Mubayi, Sudakov and Verstraete, including an application of this result to additive number theory and

- essentially tight answers to the classical Erdős unit distance and distinct distances problems in "almost all" real normed spaces of any fixed dimension.