## Algebraic Geometry Seminar

Please see the following for more related talks:

Upcoming Seminars:
• Wednesday, March 4, 2020, 3:15pm, Physics 119, Number Theory Seminar
Arithmetic loci of étale rank $1$ local systems
Helene Esnault (Freie Universitat Berline and IAS)

I’ll give our definition of them, in analogy to Simpson's bialgebraicity notion over the complex numbers, explain what special properties they have, and mention some corollaries (notably hard Lefschetz in rank $1$ in positive characteristic). Joint with Moritz Kerz

• Friday, March 20, 2020, 3:15pm, Physics 119, Department of Mathematics Seminar
TBA
Emily Witt (Kansas University)

• Friday, April 3, 2020, 3:15pm, Physics 119, Algebraic Geometry Seminar
A refined Brill-Noether theory over Hurwitz spaces
Hannah Larson (Stanford University, Mathematics)

The celebrated Brill-Noether theorem says that the space of degree d maps of a general genus g curve to P^r is irreducible. However, for special curves, this need not be the case. Indeed, for general k-gonal curves (degree k covers of P^1), this space of maps can have many components, of different dimensions (Coppens-Martens, Pflueger, Jensen-Ranganathan). In this talk, I will introduce a natural refinement of Brill-Noether loci for curves with a distinguished map C -> P^1, using the splitting type of push forwards of line bundles to P^1. In particular, studying this refinement determines the dimensions of all irreducible components of Brill-Noether loci of general k-gonal curves.

• Wednesday, April 15, 2020, 12:00pm, Physics 119, Number Theory Seminar
TBA