Comet Calendar
Algebra and Combinatorics Seminar
Wednesday, November 19, 2025 1pm to 2pm
Wednesday, November 19, 2025 1pm to 2pm
Speaker: Minh-Tâm Trinh (Howard University)
Title: Point-Counting Coincidences via HOMFLYPT and Harish-Chandra
Abstract: In 1965, Steinberg showed that the number of unipotent matrices of fixed size over a finite field is always a perfect square. In 1975, Kawanaka generalized this to a family of mysterious identities between the point counts of certain algebraic varieties appearing in Lie theory. We explain how to re-interpret Kawanaka's identity in terms of a duality in the HOMFLYPT link polynomial due to Kálmán, and hence, categorify it. We then propose a conjecture that would unify Kawanaka's result with much more recent identities discovered by Lusztig and (2021 MIT PRIMES student) Andrew Gu. The key ingredient is a map from class functions on a finite reductive group to central elements in its Hecke algebra, known as the Harish-Chandra transform.
Karl Hoblitzelle Hall (HH), 2.706
800 W. Campbell Road, Richardson, Texas 75080-3021
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