Vadim Vologodsy, University of Chicago and HSE

Title: Differential equations in number theory

Abstract: Given a linear differential equation with polynomial coefficients, one can ask if it has non-trivial solutions in algebraic functions.  A powerful approach to the study of this question is the use of the reduction to positive characteristic method and the notion of p-curvature introduced by Grothendieck and Katz (1970). I will review this notion and give some applications to complex algebraic geometry and topology.