The $p$-curvature conjecture and monodromy about simple closed loops

Joint IAS/Princeton University Number Theory Seminar
Topic:The $p$-curvature conjecture and monodromy about simple closed loops
Speaker:Ananth Shankar
Affiliation:Harvard University
Date:Thursday, May 11
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/puias/2017/0511-AnanthShankar

The Grothendieck-Katz $p$-curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its $p$-curvature vanishes modulo $p$, for almost all primes $p$. We prove that if the variety is a generic curve, then every simple closed loop has finite monodromy.