Arithmetic of differential equations

Abstract: In 1875 Fuchs asked for a criterion that determines when the solutions to an algebraic differential equation are themselves algebraic functions. Conjectural answers to this question have been given by Grothendieck and Katz, Ekedahl--Shepherd-Barron--Taylor, and Bost, in terms of the arithmetic of the differential equation's structure constants. I'll explain joint work in progress with Joshua Lam verifying these conjectures for a class of non-linear differential equations arising in algebraic geometry. This work is largely an excuse to try to better understand the arithmetic and geometry of algebraic differential equations and representations of fundamental groups of algebraic varieties.

number theory

Audience: researchers in the topic

Five College Number Theory Seminar