Upcoming Colloquia | Department of Mathematics

Geometric flexibility and rigidity of Anosov manifolds

Monday, November 10, 2025 – 4:00 pm

KEAR 212

Speaker: Alena Erchenko

We will discuss the possibility of recovering a metric from the marked boundary distance information on a compact manifold with boundary. It is analogous to the question of whether it is possible to recover a metric from the marked length of closed geodesics on a compact manifold without boundary. We will link these two questions using an isometric extension. This talk is based on joint work with Thibault Lefeuvre as well as joint work with Dong Chen and Andrey Gogolev. Read more.

Counting Ordinary and Extraordinary Hyperelliptic Curves over a Finite Field

Monday, November 17, 2025 – 4:00 pm

KEAR 212

Speaker: Jeff Thunder

Given a hyperelliptic curve defined over a finite field, there is a quantity called the a-number attached to the curve. This integer ranges from 0 to the genus and curves with a-number 0 are called "ordinary." For example, elliptic curves have genus 1 and those curves with a-number 1 are the supersingular elliptic curves ("extraordinary"). Enumerating hyperelliptic curves with given genus and/or a-number can be accomplished with more modern computing, and this leads one to conjecture probabilities for curves of given genus to have a particular a-number.In this talk we'll discuss finite fields, function fields, what it means to be a hyperelliptic curve over a finite field, and how one computes the genus and a-number. We'll recall previous work regarding the probabilities above and some methods used to address them along with some data indicating these methods may be lacking. We'll then demonstrate a relatively simple counting method, based on the theory of heights in Diophantine… Read more.