### TBA by Christina Frederick

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 18, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Christina Frederick

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- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 18, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Christina Frederick

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 11, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Rishidev Chaudhuri – UCSD

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 4, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jacob Bedrossian

- Series
- School of Mathematics Colloquium
- Time
- Thursday, May 6, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Tom Kelly – University of Birmingham – T.J.Kelly@bham.ac.uk

The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In joint work with Dong Yeap Kang, Daniela Kühn, Abhishek Methuku, and Deryk Osthus, we proved this conjecture for every sufficiently large $n$. In this talk, I will present the history of this conjecture and sketch our proof in a special case.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 29, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Lauren K. Williams – Harvard University – williams@math.harvard.edu

Two of the most famous families of polynomials in combinatorics are Macdonald polynomials and Schubert polynomials. Macdonald polynomials are a family of orthogonal symmetric polynomials which generalize Schur and Hall-Littlewood polynomials and are connected to the Hilbert scheme. Schubert polynomials also generalize Schur polynomials, and represent cohomology classes of Schubert varieties in the flag variety. Meanwhile, the asymmetric exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, which was initially introduced by Macdonald-Gibbs-Pipkin to provide a model for translation in protein synthesis. In my talk I will explain how two different variants of the ASEP have stationary distributions which are closely connected to Macdonald polynomials and Schubert polynomials, respectively. This leads to new formulas and new conjectures.

This talk is based on joint work with Corteel-Mandelshtam, and joint work with Donghyun Kim.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 22, 2021 - 12:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Po-Ling Loh – University of Cambridge – pll28@cam.ac.uk

**Please Note:** Note the unusual time: 12:00pm.

In the first part of the talk, we discuss the use of a penalized Huber M-estimator for high-dimensional linear regression. We explain how a fairly straightforward analysis yields high-probability error bounds that hold even when the additive errors are heavy-tailed. However, the parameter governing the shape of the Huber loss must be chosen in relation to the scale of the error distribution. We discuss how to use an adaptive technique, based on Lepski's method, to overcome the difficulties traditionally faced by applying Huber M-estimation in a context where both location and scale are unknown.

In the second part of the talk, we turn to a more complicated setting where both the covariates and responses may be heavy-tailed and/or adversarially contaminated. We show how to modify the Huber regression estimator by first applying an appropriate "filtering" procedure to the data based on the covariates. We prove that in low-dimensional settings, this filtered Huber regression estimator achieves near-optimal error rates. We further show that the commonly used least trimmed squares and least absolute deviation estimators may similarly be made robust to contaminated covariates via the same covariate filtering step. This is based on joint work with Ankit Pensia and Varun Jog.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 15, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Federico Bonetto – Georgia Institute of Technology – bonetto@math.gatech.edu

In 1955, Mark Kac introduced a simple model to study the evolution of a gas of particles undergoing pairwise collisions. Although extremely simplified to be rigorously treatable, the model maintains interesting aspects of gas dynamics. In recent years, together with M. Loss and others, we worked to extend the analysis to more "realistic" versions of the original Kac model. I will give a brief overview of kinetic theory, introduce the Kac model and explain the standard results on it. Finally I will present to new papers with M. Loss and R. Han and with J. Beck.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 8, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Rob Morris – National Institute for Pure and Applied Mathematics, Rio de Janeiro, Brazil – rob@impa.br

A covering system of the integers is a finite collection of arithmetic progressions whose union is the integers. The study of these objects was initiated by Erdős in 1950, and over the following decades he asked a number of beautiful questions about them. Most famously, his so-called "minimum modulus problem" was resolved in 2015 by Hough, who proved that in every covering system with distinct moduli, the minimum modulus is at most $10^{16}$.

In this talk I will present a variant of Hough's method, which turns out to be both simpler and more powerful. In particular, I will sketch a short proof of Hough's theorem, and discuss several further applications. I will also discuss a related result, proved using a different method, about the number of minimal covering systems.

Joint work with Paul Balister, Béla Bollobás, Julian Sahasrabudhe and Marius Tiba.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 1, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Yao Yao – Georgia Institute of Technology – yaoyao@math.gatech.edu

For some nonlocal PDEs, its steady states can be seen as critical points of an associated energy functional. Therefore, if one can construct perturbations around a function such that the energy decreases to first order along the perturbation, this function cannot be a steady state. In this talk, I will discuss how this simple variational approach has led to some recent progresses in the following equations, where the key is to carefully construct a suitable perturbation.

I will start with the aggregation-diffusion equation, which is a nonlocal PDE driven by two competing effects: nonlinear diffusion and long-range attraction. We show that all steady states are radially symmetric up to a translation (joint with Carrillo, Hittmeir and Volzone), and give some criteria on the uniqueness/non-uniqueness of steady states within the radial class (joint with Delgadino and Yan).

I will also discuss the 2D Euler equation, where we aim to understand under what condition must a stationary/uniformly-rotating solution be radially symmetric. Using a variational approach, we settle some open questions on the radial symmetry of rotating patches, and also show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial (joint with Gómez-Serrano, Park and Shi).

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 18, 2021 - 11:00 for 1 hour (actually 50 minutes)
- Location
- https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
- Speaker
- Jinchao Xu – Pennsylvania State University – xu@math.psu.edu

Piecewise polynomials with certain global smoothness can be given by traditional finite element methods and also by neural networks with some power of ReLU as activation function. In this talk, I will present some recent results on the connections between finite element and neural network functions and comparative studies of their approximation properties and applications to numerical solution of partial differential equations of high order and/or in high dimensions.