Abstracts

Week of October 12, 2025

October 13, 2025
Geometric Analysis and Application Stable Bernstein problem in certain positively curved manifolds 3:45pm -
KT 906

Abstract: We formulate a stable Bernstein problem in two types of positively curved manifolds. We completely solved for one type in all dimensions and partially solved for the other in low dimensions, leading to several interesting corollaries.
October 14, 2025
Geometry, Symmetry and Physics Trace of the affine Hecke category 4:30pm -
KT 801

The affine Hecke category, defined using affine Soergel bimodules, categorifies the affine Hecke algebra. I will compare the derived horizontal trace of the affine Hecke category with the elliptic Hall algebra, and with the derived category of the commuting stack. In particular, I will describe certain explicit generators for the trace category and some categorical commutation relations between these. This is a joint work with Andrei Negut.
Geometry & Topology Incompressible surfaces in closed hyperbolic manifolds 4:30pm -
KT 203

In 2009, Kahn and Markovic proved the Surface Subgroup Theorem, and they constructed a ubiquitous collection of \pi_1-injective immersed surfaces in closed hyperbolic 3-manifolds. Hamenstadt later showed that any cocompact lattice of some simple rank 1 Lie group other than SO(2m,1) (m >= 1) has a surface subgroup. Recently, we constructed \pi_1-injective immersed surfaces in closed hyperbolic 2n-manifolds, which addresses the cases missing from Hamenstadt’s work. This is joint work with Jeremy Kahn.
October 17, 2025
Friday Morning Seminar Friday Morning Seminar 10:00am -
KT 801

We have impromptu and (sometimes) scheduled talks, on topics in probability, combinatorics, geometry, and dynamics.

Everyone is welcome!