## EVENT DETAILS AND ABSTRACT

**Algebraic Geometry Seminar**
**Title:** Maximal Brill-Noether loci

**Speaker:** Asher Auel

**Speaker Info:** Dartmouth College

**Brief Description:**

**Special Note**:

**Abstract:**

Brill-Noether theory answers the question of whether a general curve of genus g admits a linear system of rank r and degree d. A refined Brill-Noether theory hopes to answer the question of whether a general such curve also admits a linear system of rank r’ and degree d'. In other words, we want to know about the relative position between Brill-Noether loci in the moduli space of curves of genus g. I'll explain a strategy for distinguishing Brill-Noether loci by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill-Noether loci with respect to containment. Via an analysis of the stability of Lazarsfeld-Mukai bundles, we obtain new lifting results for linear systems of rank 3 which suffice to prove the maximal Brill-Noether loci conjecture in genus up to 23. This is joint work with Richard Haburcak.

**Date:** Friday, April 21, 2023

**Time:** 11:00am

**Where:** Tech MG28

**Contact Person:** Yuchen Liu

**Contact email:** yuchenl@northwestern.edu

**Contact Phone:**

Copyright © 1997-2024
Department of Mathematics, Northwestern University.