Title: Geometric Casselman-Shalika in mixed characteristic Abstract: I will present joint work with Ashwin Iyengar and Konrad Zou, where we proved a geometric analog of the (local) Casselman-Shalika formula for split connected reductive groups over mixed characteristic local fields. This formula captures properties of Fourier coefficients of automorphic functions that are fundamental to the Langlands […]
Euler systems and spherical functions. (Continued)
Title: The geometry and topology of lower bounds on scalar curvatureAbstract: In this talk, I will discuss some recent results about controlling the geometry and topology of manifolds from a (positive) lower bound on their scalar curvature.
Title: Curves on Varieties and the Degree of Irrationality.Abstract: Inspired by the Noether-Lefschetz theorem, it has been conjectured that the degree of any curve on a (very) general complete intersection variety is divisible by the degree of the variety itself. In this talk, we present a weaker version of this conjecture. Using this result, we confirm a […]
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 […]