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. Delve into the definition of periodic pencils of flat connections on smooth algebraic varieties and discover their remarkable properties. Learn about notable examples such as Knizhnik-Zamolodchikov, Dunkl, Casimir connections, and equivariant quantum connections for conical symplectic resolutions. Examine the behavior of p-curvature operators in characteristic p and understand how they relate to commuting endomorphisms. Gain insights into computing eigenvalues of p-curvature for various examples and learn about the regular singularities of periodic pencils of connections. This hour-long presentation, hosted by the Institut des Hautes Etudes Scientifiques (IHES), covers joint work with Alexander Varchenko and offers a deep dive into advanced mathematical concepts at the intersection of algebraic geometry and differential equations.