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Title:
Opers — what they are and what they are good for?
Speaker:
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 spectra 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.
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