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Analytic Langlands correspondence for PGL(2) on P^1 with parabolic structures over local fields
Pavel Etingof, Edward Frenkel, David Kazhdan
We continue to develop the analytic Langlands program for curves over local fields initiated in arXiv:1908.09677, arXiv:2103.01509 following a suggestion of Langlands and a work of…
Hecke operators and analytic Langlands correspondence for curves over local fields
Pavel Etingof, Edward Frenkel, David Kazhdan
We construct analogues of the Hecke operators for the moduli space of G-bundles on a curve X over a local field F with parabolic structures at finitely many points. We conjecture t…
An analytic version of the Langlands correspondence for complex curves
Pavel Etingof, Edward Frenkel, David Kazhdan
The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Langlands asked whether it is possible to construct…
Geometric Langlands Correspondence Near Opers
Edward Frenkel, Constantin Teleman
We extend the categorical geometric Langlands correspondence from the locus of opers in the stack of de Rham local systems on a smooth projective algebraic curve to the formal neig…
Gromov-Witten Gauge Theory I
Edward Frenkel, Constantin Teleman, A. J. Tolland
We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of th…
A rigid irregular connection on the projective line
Edward Frenkel, Benedict Gross
In this paper we construct a connection on the trivial G-bundle on the projective line for any simple complex algebraic group G, which is regular outside of the points 0 and infini…