Title: Unipotent Representations of Real Reductive Groups and Mixed Hodge Modules Abstract: Let Pi(G) denote the set of irreducible unitary representations of a semisimple Lie group G. A fundamental problem in representation theory is to describe the structure of this set. In previous joint work with Losev and Matvieievskyi, we have defined a class of […]
Title: A Khovanov-like Categorification of the Four Color TheoremAbstract: The four color theorem states that each bridgeless trivalent planar graph has a proper 4-face coloring. It can be generalized to certain types of CW complexes of any closed surface for any number of colors, i.e., one looks for a coloring of the 2-cells (faces) of […]
Langlands functoriality and stable transfer. (Continued.)
Title: On isolated singularities and generic regularity of min-max CMC hypersurfacesAbstract: Smooth constant mean curvature (CMC) hypersurfaces serve as effective tools to study the geometry and topology of Riemannian manifolds. In high dimensions however, one in general must account for their singular behaviour. I will discuss how such hypersurfaces are constructed via min-max techniques and […]
Title: Nonabelian Fourier kernels on SL₂ and GL₂ Abstract: I will present my collaborative work with Ngô on explicit formulas for the nonabelian Fourier kernels on SL₂ and GL₂, as conjectured by Braverman and Kazhdan. Additionally, I will discuss its connection to the orbital Hankel transform studied by Ngô.
Title: Twisted Intermediate Jacobian Fibrations.Abstract:In this talk, I will report on a joint work in progress with D. Mattei and E. Shinder, where we construct, using Hodge modules, a group scheme that can be thought of as the intermediate Jacobian of a certain complete family of cubic threefolds. We show that the group scheme acts on […]
Title: Rectification of Coalgebras Abstract: There are two ways of talking about homotopy coherent algebras. One is to use model theoretic ideas: given a nice model category (C, W), one gets a right induced model structure on Alg(C). Second, one can use infinity category methods. Any nice model category (C, W) has an infinity categorical […]
Title: Transfer operators for the relative trace formula. Abstract: Transfer operators are operators between spaces of test measures on different groups, whose duals are supposed to realize the transfer of (stable) characters predicted by Langlands functoriality. I will explain how this concept generalizes to the setting of the relative trace formula, and present some formulas […]
Tittle: Partial regularity for Lipschitz solutions to the minimal surface system Abstract: The minimal surface system is the Euler-Lagrange system for the area functional of a high codimension graph and reduces to the minimal surface equation in the case that the codimension is one. Though the regularity theory for the minimal surface equation is well understood, […]
Title: Formalizing ∞-Category Theory in Lean
Title: The local theta correspondence and functoriality Abstract: In a letter to Howe, Langlands conjectured that the local theta correspondence is an instance of Langlands functoriality, e.g., it should preserve L-packets. Unfortunately, this was false. As a remedy, Adams conjectured that instead of L-packets, the local theta correspondence should preserve Arthur packets. Mœglin showed that […]