### TBA by Dmitri Chklovskii

- Series
- School of Mathematics Colloquium
- Time
- Thursday, December 5, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Dmitri Chklovskii – NYU and the Flatiron Institute

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- Series
- School of Mathematics Colloquium
- Time
- Thursday, December 5, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Dmitri Chklovskii – NYU and the Flatiron Institute

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 21, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Evgeny Mukhin – Indiana University

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 7, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Rachel Greenfeld – Northwestern University

- Series
- School of Mathematics Colloquium
- Time
- Friday, October 25, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005/006
- Speaker
- Peter Sarnak – Princeton University – sarnak@math.princeton.edu

Endowing a finite combinatorial graph with lengths on its edges defines singular 1-dimensional Riemannian manifolds known as metric graphs. The spectra of their Laplacians have been widely studied. We show that these spectra have a structured linear part described in terms of arithmetic progressions and a nonlinear "random" part which is highly linearly and even algebraically independent over the rationals. These spectra give rise to exotic crystalline measures ("Generalised Poisson Summation Formulae") and resolve various open problems concerning the latter. This is a joint work with Pavel Kurasov.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 10, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Caroline Klivans – Brown University

There is a rich history of domino tilings in two dimensions. Through a variety of techniques we can answer questions such as: how many tilings are there of a given region or what does a random tiling look like? These questions and their answers become significantly more difficult in dimension three and above. Despite this curse of dimensionality, I will discuss recent advances in the theory. I will also highlight problems that still remain open.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 3, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Yanyan Li – Rutgers University – yyli@rutgers.edu

A harmonic function of two variables is the real or imaginary part of an analytic function. A harmonic function of $n$ variables is a function $u$ satisfying

$$

\frac{\partial^2 u}{\partial x_1^2}+\ldots+\frac{\partial^2u}{\partial x_n^2}=0.

$$

We will first recall some basic results on harmonic functions: the mean value property, the maximum principle, the Liouville theorem, the Harnack inequality, the Bocher theorem, the capacity and removable singularities. We will then present a number of more recent results on some conformally invariant elliptic and degenerate elliptic equations arising from conformal geometry. These include results on Liouville theorems, Harnack inequalities, and Bocher theorems.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, September 19, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jen Hom – Georgia Tech

Under the operation of connected sum, the set of three-manifolds form a monoid. Modulo an equivalence relation called homology cobordism, this monoid (of homology spheres) becomes a group. What is the structure of this group? What families of three-manifolds generate (or don’t generate) this group? We give some answers to these questions using Heegaard Floer homology. This is joint work with (various subsets of) I. Dai, K. Hendricks, M. Stoffregen, L. Truong, and I. Zemke.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, September 5, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Alexander Razborov – The University of Chicago

Combinatorics was conceived, and then developed over centuries as a discipline about finite structures. In the modern world, however, its applications increasingly pertain to structures that, although finite, are extremely large: the Internet network, social networks, statistical physics, to name just a few. This makes it very natural to try to think of the "limit theory" of such objects by pretending that "very large" actually means "infinite". This mathematical abstraction turns out to be very useful and instructive.

After briefly reviewing the basics of the theory (graphons and flag algebras), I will report on some more recent developments. Time permitting, we will discuss the most general form of the theory suitable for arbitrary combinatorial structures (peons and theons), its applications to the theory of quasi-randomness and its applications to machine learning.

The first two topics are based on joint work with L. Coregliano, and the third one on a recent paper by Coregliano and Malliaris.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, August 22, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- William Layton – University of Pittsburgh

Over the last 40 years there have been great advances in computer hardware, solvers (methods for solving Ax=b and F(x)=0), meshing algorithms, time stepping methods, adaptivity and so on. Yet accurate prediction of fluid motion (for settings where this is needed) is still elusive. This talk will review three major hurdles that remain: ensemble simulations, time accuracy and model stagnation. Three recent ideas where numerical analysis can help push forward the boundary between what can be done and what can't be done will be described. This talk is based on joint work with many. It should be completely understandable by grad students with a basic PDE class.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 11, 2024 - 11:00 for
- Location
- Skiles 005
- Speaker
- Andre Neves – University of Chicago – aneves@math.uchicago.edu

The asymptotic behavior of closed geodesic on negatively curved spaces occupies a central place in Riemannian geometry. Minimal surfaces are higher dimensional analogies of geodesics and I will talk about some recent developments regarding the growth rate of minimal surfaces in negatively curved manifolds.