Past Events

Richard Stanley asked in 1995 whether a tree is determined up to isomorphism by its chromatic symmetric function. This question remains unanswered and frequently keeps the speaker awake at night. Our approach to understanding the strength of the...

The Poisson boundary of a random walk on a group is a probability space used to study the long-term behavior of the random walk. Because the group naturally acts on the Poisson boundary, various questions regarding the structure of this action can be...

A fundamental aim of evolutionary biology is to describe and explain biodiversity patterns; this aim centers around questions of how many "species" exist, where they are most/least abundant, how this distribution is changing over time, and why...

A matrix is called totally positive if all of its minors are positive. These matrices are important in mathe- matics, but checking whether a large matrix is totally positive can be challenging. In this talk, we explore whether certain matrices...

The least quadratic non-residue has been a central problem in number theory for centuries. The average least quadratic non-residue was explored by Erdős in the 1960s, and many extensions of this problem such as to the average least character non...

In this talk, we will study the first and second twisted moments of some Rankin-Selberg convolution L-functions of an automorphic form of prime power level. Our first moment result can be used to prove that automorphic forms of suitable weight and...

The interactions among species in a food web or food chain are inherently complex. Mathematical models provide a framework to closely represent the dynamics observed in ecosystems. However, capturing this complexity within a single mathematical setup...

The Hecke orbit conjecture predicts that Hecke symmetries characterize the central foliation on Shimura varieties over an algebraically closed field k of characteristic p. The original conjecture predicts that on the mod p reduction of a Shimura...

The computer is taking over. AND, in many branches of applied mathematics and statistics we hear 'why bother to prove theorems? simulations and numerical approximation are easier and better for real problems'. NOT SO FAST; I will present a collection...

In recent years, there has been growing promise in coupling machine learning methods with domain-specific physical insights to solve scientific problems based on partial differential equations (PDEs). However, there are two critical bottlenecks that...