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Algebra Seminar

Monday, April 15, 2024 - 3:30pm

Kiran Kedlaya

UCSD & IAS Princeton


University of Pennsylvania

DRL 4N30

Tea will be served at 3pm in the Math Lounge, DRL, 4th floor.

With Yongyuan Huang and Jun Bo Lau, we recently completed a census of genus-6 curves over the field F_2, and are working on a similar census in genus 7. This uses Mukai's "flowcharts" for describing canonical curves in this genera. We discuss some of the key features of this classification; some aspects of computational group theory required to convert this classification into tractable computations; and some applications of the results, including relative class number problems for function fields, gonality of curves over finite fields (work of
Faber-Grantham-Howe), and cohomology of modular curves (work of Canning-Larson and Bergstrom-Canning-Petersen-Schmitt).