Vertex algebra constructions for (analytic) geometric Langlands in genus zero by Davide Gaiotto

“…Abstract We employ two-dimensional chiral algebra techniques to produce solutions of certain differential and integral equations which occur in the context of the Analytic Geometric Langlands Program. In particular, we build “Multiplication Kernels” K 3(x, x′, x′′) which intertwine the action of s l 2 $$ \mathfrak{s}{\mathfrak{l}}_2 $$ Gaudin Hamiltonians on three sets of variables.…”
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Geometrization of the Satake transform for mod p Hecke algebras by Robert Cass, Yujie Xu

“…Our methods involve the constant term functors inspired from the geometric Langlands program, and we also treat the case of reductive groups in equal characteristic. …”
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