Quantum geometric Langlands as a fully extended TFT

Abstract: I will survey several recent works realizing Betti geometric Langlands and its quantization as fully extended TFT's. In physics terms this is most closely related to the Kapustin-Witten twist of N=4 d=4 SYM at generic values of \Psi.

I will outline numerous applications to quantum topology, most notably to a conjecture of Witten on finite-dimensionality of skein modules, a conjecture of Bonahon-Wong concerning skein modules at root-of-unity parameters, a proposal of Ben-Zvi concerning cluster varieties and factorization homology, and an appearance of the type-A spherical DAHA from a once-marked torus.

Finally, I will present a novel conjectural appearance of S-duality in the study of skein modules of 3-manifolds.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.