Periodic Pencils of Flat Connections and Their p-Curvature

Explore a comprehensive lecture on periodic pencils of flat connections and their p-curvature, delivered by Pavel Etingof from MIT at the M-Seminar, Kansas State University. Delve into the definition and properties of periodic pencils of flat connections on smooth algebraic varieties, examining their invariance under certain shifts. Discover numerous interesting examples, including Knizhnik-Zamolodchikov, Dunkl, Casimir connections, and equivariant quantum connections for conical symplectic resolutions with finitely many torus fixed points. Investigate the behavior of p-curvature operators in characteristic p and their isospectrality to specific commuting endomorphisms. Learn how this relationship enables the computation of p-curvature eigenvalues for various examples and proves that periodic pencils of connections always have regular singularities. Gain insights into this joint work with Alexander Varchenko, presented over the course of 1 hour and 26 minutes.