q-Opers — what they are and what are they good for?

Abstract: I will introduce the new geometric object - (G,q)-opers on a Riemann surface where G is a simple simply connected Lie algebra. I will describe their applications in geometric Langlands and integrable systems. Using the formalism of (G,q)-opers we can describe spectrum of quantum integrable models, like XXZ spin chains and their generalizations in representation theory (so called quantum/classical duality). As a different application we can study wall crossing transformations between fundamental solutions of Fuchsian ODEs with regular singularities (ODE/IM correspondence) using (G,q)-oper connections.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar