## 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*

Jordan Ellenberg (University of Wisconsin-Madison)
- TBA

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