Starting with Langlands' original program, there have been proposed numerous versions of Langlands conjectures in various settings, obtained by a sequence of analogies. One of the striking features of the versions for Riemann surfaces is their connections to quantum field theory, which has led to significant progress in this setting. I will describe a new unifying version of the geometric Langlands conjecture which interpolates between all other geometric versions. In particular, this allows to apply ideas from quantum field theory to new settings. As a consequence, we resolve a number of long-standing questions in geometric Langlands and obtain a purely spectral description of automorphic forms for algebraic curves over finite fields, which in particular gives a refinement of V. Lafforgue's spectral decomposition.
Math-Physics Joint Seminar
Friday, December 2, 2022 - 3:30pm
Nikita Rozenblyum
University of Chicago
Other Events on This Day
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Betti Langlands discussion group
Math-Physics Joint Seminar
11:00am