Rational points on curves over finite fields and their asymptotic

Abstract: Curves over finite fields with many rational points have been of interest for both theoretical reasons and for applications. To obtain such curves with large genus various methods have been employed in the past. One such method is by means of explicit recursive equations and will be the emphasis of this talk. The recursive nature of these towers makes them very special and in fact all good examples have been shown to have a modular interpretation of some sort. In this talk I will try to give an overview of the landscape of explicit recursive towers and their modularity.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca