ONLINE from the Institute of Advanced Study
Image: Eecc, Wikimedia Commons
The 2021 Clay Research Conference will be live-streamed from the Institute of Advanced Study on Thursday, September 30th. To register for this online event, please email Naomi Kraker. Access details for the Zoom conference will be sent out prior to the event using the email address you provide.
13:30 László Székelyhidi (IAS, Leipzig), Convex Integration and Synthetic Turbulence (Video)
16:00 Edward Witten (IAS), Gauge Theory and the Analytic Approach to Geometric Langlands (Video)
17:10 Camillo DeLellis (IAS), The Works of Buckmaster, Isett and Vicol in Incompressible Fluid Dynamics (Video)
Thomas Clay, Presentation of the Clay Research Award to Tristan Buckmaster, Philip Isett and Vlad Vicol.
All times are EDT.
László Székelyhidi, Institute for Advanced Study and Leipzig University
Title: Convex Integration and Synthetic Turbulence
Abstract: In the past decade convex integration has been established as a powerful and versatile technique for the construction of weak solutions of various nonlinear systems of partial differential equations arising in fluid dynamics, including the Euler and Navier-Stokes equations. The existence theorems obtained in this way come at a high price: solutions are highly irregular, non-differentiable, and very much non-unique as there is usually infinitely many of them. Therefore this technique has often been thought of as a way to obtain mathematical counterexamples in the spirit of Weierstrass’ non-differentiable function, rather than advancing physical theory; “pathological”, “wild”, “paradoxical”, “counterintuitive” are some of the adjectives usually associated with solutions obtained via convex integration. In this lecture I would like to draw on some recent examples to show that there are many more sides to the story, and that, with proper usage and interpretation, the convex integration toolbox can indeed provide useful insights for problems in hydrodynamics.
Edward Witten, Institute for Advanced Study
Title: Gauge Theory and the Analytic Approach to Geometric Langlands
Abstract: Recently P. Etingof, E. Frenkel, and D. Kazhdan, following earlier contributions by R. Langlands and J. Teschner, described an “analytic” approach to the geometric Langlands correspondence, in which the main ingredients are quantum states and operators acting on them rather than categories and functors. In this talk, I will review the gauge theory approach to the “categorical” version of geometric Langlands, and then, following the paper arXiv:2107.01732 with D. Gaiotto, I will explain how the same ingredients can be arranged differently to give a gauge theory interpretation of the “analytic” version of geometric Langlands.