Title: Around the notion of p-curvature.


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. Then I will describe  a parallel theory, developed by Pan and Camargo (2022), for topological local systems on p-adic analytic varieties. Finally, I will sketch a construction due to Bhatt, Kanaev, Mathew, Zhang, and myself that interpolates 
between the two theories.

Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=b4f1e7b6-cb0d-43ab-a021-b23300db20a6