Topological Langlands duality for 3-manifolds

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• David Jordan (Edinburgh)
• Wednesday 26 October 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

Langlands duality originated in number theory, was translated into algebraic geometry of projective curves by Beilinson, Drinfeld, Arinkin, Gaitsgory and many others; and subsequently re-interpreted in quantum field theory by Kapustin and Witten.

In this talk I’ll explain a novel conjectural appearance of Langlands duality in the quantum topology of 3-manifolds via so-called skein modules, which are deformation quantizations of character varieties of 3-manifolds. One pleasant feature in this context is that Langlands duality is very elementary: it is the assertion that two integers—computed from M using a group G and its Langlands dual—are equal. The conjecture and the evidence I’ll present is joint work with various of Ben-Zvi, Gunningham, Safronov, Vazirani and Yang.

This talk is part of the Differential Geometry and Topology Seminar series.

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