# AMS Student Chapter Seminar

The AMS Student Chapter Seminar is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.

Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.

The schedule of talks from past semesters can be found here.

## Spring 2019

### February 6, Xiao Shen (in VV B139)

Title: Limit Shape in last passage percolation

Abstract: Imagine the following situation, attached to each point on the integer lattice Z^2 there is an arbitrary amount of donuts. Fix x and y in Z^2, if you get to eat all the donuts along an up-right path between these two points, what would be the maximum amount of donuts you can get? This model is often called last passage percolation, and I will discuss a classical result about its scaling limit: what happens if we zoom out and let the distance between x and y tend to infinity.

### February 13, Michel Alexis (in VV B139)

Title: An instructive yet useless theorem about random Fourier Series

Abstract: Consider a Fourier series with random, symmetric, independent coefficients. With what probability is this the Fourier series of a continuous function? An $L^{p}$ function? A surprising result is the Billard theorem, which says such a series results almost surely from an $L^{\infty}$ function if and only if it results almost surely from a continuous function. Although the theorem in of itself is kind of useless in of itself, its proof is instructive in that we will see how, via the principle of reduction, one can usually just pretend all symmetric random variables are just coin flips (Bernoulli trials with outcomes $\pm 1$).

### February 20, Geoff Bentsen

Title: An Analyst Wanders into a Topology Conference

Abstract: Fourier Restriction is a big open problem in Harmonic Analysis; given a "small" subset [itex]E[itex] of [itex]R^d[itex], can we restrict the Fourier transform of an [itex]L^p[itex] function to [itex]E[itex] and retain any information about our original function? This problem has a nice (somewhat) complete solution for smooth manifolds of co-dimension one. I will explore how to start generalizing this result to smooth manifolds of higher co-dimension, and how a topology paper from the 60s about the hairy ball problem came in handy along the way.

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### March 6, Working Group to establish an Association of Mathematics Graduate Students

Title: Math and Government

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