(RESCHEDULED)Combinatorics and Algebra Seminar-Link Polynomials and Meridian Twists in Algebraic Geometry

Title: Link Polynomials and Meridian Twists in Algebraic Geometry
Speaker: Minh-Tâm Trinh, Howard
Date and time: Tuesday, February 3, 4–5 pm
Place: Rome 206, GWU

Abstract:  Steinberg showed that the number of unipotent elements in a finite reductive group, like GL(n, q), is always a perfect square. Kawanaka generalized this fact to a family of mysterious identities between the point counts of algebraic varieties over finite fields. We show that surprisingly, Kawanaka’s result implies a “meridian twisting” identity for the HOMFLYPT link invariant due to Kálmán. This relies on a formula expressing the HOMFLYPT trace on the Hecke algebras of the groups GL(n, q) in terms of the Springer fibers studied in geometric representation theory. If time permits, we will explain how these ideas suggest a purely topological analogue of Kawanaka’s theorem, for varieties over the complex numbers.