Non-abelian cohomology, differential equations, and p-curvaturesArithmetic Geometry and Representation Theory Research Seminar

by Josh Lam

Friday Nov 21, 2025, 2:05 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

One central aspect of algebraic geometry is that the cohomology
of algebraic varieties admit many extra structures as compared with that
of, say, topological spaces. I will discuss some of these structures in the
setting of "non-abelian cohomology", as pioneered by Simpson, and the new
features that arise; we'll see that they are closely related to classical
questions about differential equations such as the Schlesinger system. In
particular, I'll talk about the proof of a conjecture of
Ekedahl--Shepherd-Barron--Taylor's and Bost's in many new cases, which is
about the p-curvatures of differential equations such as Schlesinger's.
This is joint work with Daniel Litt, following ideas of Kisin, Menzies, and
Papaioannou.