### Speaker

Prof.
Daniel Litt
(University of Toronto)

### Description

The classical Grothendieck-Katz $p$-curvature conjecture gives an arithmetic criterion for the solutions to an algebraic linear ODE to be algebraic functions. We formulate a version of the $p$-curvature conjecture for certain non-linear ODEs arising from algebraic geometry (for example, the Painlevé VI equation or the Schlesinger system), which implies the classical conjecture, and prove it for "Picard-Fuchs initial conditions." The proof is inspired in part by Katz's resolution of the classical p-curvature conjecture for Picard-Fuchs equations, and in part by Esnault-Groechenig's recent resolution of the classical conjecture for rigid $\mathbb{Z}$-local systems. This is joint work with Josh Lam.