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SUMMARY:Analytic Langlands correspondence for complex curves
DTSTART;VALUE=DATE-TIME:20210601T013000Z
DTEND;VALUE=DATE-TIME:20210601T024500Z
DTSTAMP;VALUE=DATE-TIME:20240417T032200Z
UID:indico-contribution-5716@indico.ipmu.jp
DESCRIPTION:Speakers: Edward Frenkel (U.C. Berkeley)\nThe Langlands corres
pondence for complex curves has been traditionally formulated in terms of
sheaves rather than functions. Together with Pavel Etingof and David Kazhd
an (arXiv:1908.09677\, arXiv:2103.01509)\, we have formulated an analytic
(or function-theoretic) version as a spectral problem for an algebra of co
mmuting operators acting on half-densities on the moduli space Bun_G of G-
bundles over a complex algebraic curve. This algebra is generated by the g
lobal differential operators on Bun_G (holomorphic and anti-holomorphic qu
antum Hitchin Hamiltonians) as well as integral operators\, which are anal
ytic analogues of the Hecke operators of the classical Langlands correspon
dence. We conjecture that the joint spectrum of this algebra (properly und
erstood) can be identified with the set of opers for the Langlands dual gr
oup of G whose monodromy is in the split real form (up to conjugation). Fu
rthermore\, we give an explicit formula relating the eigenvalues of the He
cke operators and the global differential operators.\n\nhttps://indico.ipm
u.jp/event/387/contributions/5716/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5716/
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