The Simons Center for Geometry and Physics is pleased to announce the following talks during the week of Monday, January 5th - Saturday, January 10th
SCGP Colloquium by Sam Raskin
Wednesday, January 7th at 2:30pm in 102
Title: Quantum geometric Langlands and TQFTs
Abstract: Kapustin and Witten proposed that quantum geometric Langlands should be interpreted as S-duality between two 4-dimensional TQFTs – certain twists of maximally supersymmetric Yang-Mills for Langlands dual gauge groups. I'll describe a "Betti" variant of the quantum geometric Langlands as an equivalence of 4d TQFts. I'll provide some expectations for how the theory should develop, and indicate how everything works in the abelian case. In the non-abelian case, the anticipated theory is related to non-compact Chern-Simons and quantization of modlui space. One fun aspect is the inherently analytic nature of the story. This is joint work with Peter Scholze.
Program Talk: Olivier Biquard
Thursday, January 8th at 11:15am in SCGP 313
Speaker: Olivier Biquard
Title: Gravitational instantons, Hermitian geometry and stability
Abstract: Gravitational instantons are finite energy Ricci flat complete 4-manifolds. They are completely understood in the Kähler setting, but remain mysterious in general, with old questions going back to the 90's. There are some exciting development in the field at the moment, and I shall explain some recent results using Hermitian geometry.
Math Colloquium by Sam Raskin
Thursday, January 8th at 2:30pm in 313
Title: Recent progress in geometric Langlands
Abstract: By analogy with Langlands's conjectures in arithmetic, Beilinson and Drinfeld conjectured that D-modules on the space of G-bundles on an algebraic curve are the same as (certain) coherent sheaves on the space of local systems on the same curve, but for the Langlands dual group. We will discuss our recent work, joint with Gaitsgory and partially joint with Arinkin, Beraldo, Campbell, Chen, Faergeman, Lin, and Rozenblyum, verifying this conjecture and some related questions. However, the real focus for the talk will be various starting points in the theory, with the hope that this helps to give outsiders some feeling for what the subject is about.
Program Talk: Bernardo Araneda
Friday, January 9th at 2:00pm in SCGP 313
Speaker: Bernardo Araneda
Title: Ernst equations, Kähler structures, and Einstein-Maxwell instantons
Abstract: The Ernst formulation of the Einstein equations provides a solution-generating technique and leads to infinite-dimensional hidden symmetries encoded in the Geroch group. Other solution-generating methods are based on the existence of complex structures, such as the Gibbons-Hawking ansatz and Toda constructions. I will present a novel interplay between these two methods. As an application, the Einstein-Maxwell version of the Euclidean Black Hole Uniqueness Conjecture will be addressed. Based on joint work with Maciej Dunajski.