MATH Seminar

Title: Arithmetic Geometry and Stacky Curves
Seminar: Algebra
Speaker: Andrew Kobin of Emory University
Contact: Andrew Kobin, ajkobin@emory.edu
Date: 2023-09-12 at 4:00PM
Venue: MSC N302
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Abstract: Solutions to many problems in number theory can be described using the theory of algebraic stacks. In this talk, I will describe a few Diophantine equations, such as the ``generalized Fermat equation'' $Ax^{p} + Bx^{q} = Cz^{r}$, whose integer solutions can be found using an appropriate stacky curve: a curve with extra automorphisms at prescribed points. I will also describe how stacky curves can be used to study rings of modular forms both classically and in characteristic $p$. Parts of the talk are joint work in progress with Juanita Duque-Rosero, Chris Keyes, Manami Roy, Soumya Sankar and Yidi Wang, and separately with David Zureick-Brown.