Introduction to Research Seminar

AMS Intro to Research Seminar has returned to Vincent 570! Find us Wednesdays at 12:20.

4/20/22 - Speaker: Gregg Musikker

Title: A Crash Course on Kuo Condensation and its Applications in Combinatorics

4/13/22 - Speaker: Montie Avery

Title: Front propagation and diffusive stability

Abstract: What happens when a background state becomes unstable in a large physical system? Often localized perturbations grow and spread outward, creating a new nontrivial structure in their wake. The fundamental question is then to predict the speed of this spreading process and the selected structure left behind. This question is answered by the marginal stability conjecture, which relates predictions of spreading speeds to certain properties of an associated eigenvalue problem. I will briefly introduce the marginal stability conjecture, and then give a flavor of the kind of tools my advisor and I used to prove it. These tools are diffusive stability estimates, which aim to prove stability of special solutions of certain nonlinear partial differential equations, when the linearized part of the equation only exhibits very slow decay in time.

3/30/22 - Speaker: Peter Polacik

Title: Studies of partial differential equations: some results and examples in the qualitative theory

Abstract: The purpose of this talk is to give the students in the audience a flavor of qualitative theory of partial differential equations (PDEs), focusing on a class of nonlinear parabolic PDEs. These are evolutionary equations and one can naturally ask questions as one would when dealing with ordinary differential equations. For example, do bounded solutions approach an equilibrium as time approaches infinity? In other questions, we remember we are dealing with PDEs, which have both spatial and temporal variables, and an interplay between spatial and temporal structures of solutions gets some attention. No prior knowledge of PDEs is needed for this talk.

3/2/22 - Speaker: Dihua Jiang

Title: An Introduction to the Langlands Program

Abstract: The Langlands Program is the core of the modern theory of automorphic forms, which consists of a series of conjectures proposed

by R. Langlands. Those conjectures connect Number Theory, Algebraic Geometry, Harmonic Analysis and Representations of Lie Groups.

In this talk, I will give an introduction to some aspects of the Langlands program, which are closely related to my own work.

11/3/21 - Speaker: Paul Garrett

Title: PDE and zeros of the zeta function

12/1/21 - Panel: The combinatorics group!

12/8/21 - Speaker: Patty Commins

Title: The Interplay Between Representations of Reflection Groups and Some Associated Algebras

Summary: Reflection Groups are a well-studied family of groups with rich connections to several areas of math. In this talk, we will explore reflection groups as well as two algebras which arise from them: Solomon's descent algebra and the face algebra. We will examine how these three structures interact, considering a question about their representation theory. Do not worry if you haven't seen representation theory before! We will focus on the big picture ideas, aiming to demonstrate some of the ways combinatorics can be useful in understanding algebraic structures.