Geometric Methods in Representation Theory Seminar

Mode: In-person Title: Blow-ups and the quantum spectrum of surfaces Abstract: The cup product of ordinary cohomology describes how submanifolds of a manifold intersect each other. Gromov-Witten invariants give rise to quantum product and quantum cohomology, which describe how subspaces … Read more

Linear spaces of matrices of bounded rank Abstract. A classical problem in linear algebra is to classify linear spaces of matrices such that no element of the space has full rank. Work of Eisenbud and Harris showed that the problem … Read more

N-spherical functors and categorification of Euler’s continuants Abstract. Euler’s continuants are universal polynomials expressing the numerator and denominator of a finite continued fraction in terms of its entries. Remarkably, they make an appearance in the very foundations of category theory: … Read more

Title: Hitchin WKB problem and Geometric P=W conjecture in rank 2 Abstract: After reviewing nonabelian Hodge and Riemann--Hilbert correspondences over curves, I state two closely related open problems concerning their large-scale behavior. I then propose an answer to these questions … Read more

Title: Monotone links in the DAHA and EHA Abstract: Morton and Samuelson related certain skein algebras on the torus with the double affine Hecke algebra (DAHA) and the elliptic Hall algebra (EHA). We use this construction to study link homology … Read more

Title: Equivalence of Hecke Categories with Deeper Level Structures Abstract: Inspired by the theory of positive depth representations of p-adic reductive groups, we study Hecke categories associated to certain open compact subgroups smaller than the Iwahori subgroup. In this talk, … Read more

Row-Column Mirror Symmetry for Colored Torus Knot Homology Abstract. The HOMFLYPT polynomial is a 2-variable link invariant generalizing the celebrated Jones polynomial and other Type A quantum link polynomials. Its construction passes through a Hecke algebra representation of the braid … Read more

On the Poisson summation conjecture Abstract: Braverman, Kazhdan, Lafforgue, Ngo, and Sakellaridis have conjectured that Fourier analysis on a vector space is but the first example of a larger phenomenon. More generally, one should have Schwartz spaces, Fourier transforms, and, … Read more

Cellular pavings of convolution fibers and applications Abstract. A convolution morphism is the geometric analogue of a convolution of functions in a Hecke algebra. The properties of fibers of convolution morphisms are used in a variety of ways in the … Read more

Semi-infinite flag manifolds, space of maps, and quantum K-groups of flag manifolds Abstract: We first recall the Plucker relations, that yield a description of a(n open) space of maps from a projective line to a (partial) flag manifolds. Then, we … Read more