Algebra and Algebraic Geometry Seminar Spring 2025

The seminar normally meets 2:30-3:30pm on Fridays, in the room Van Vleck B325.

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Spring 2025 Schedule

date	speaker	title	host/link to talk
January 31	Jakub Koncki (Warsaw)	SSM Thom polynomials of multisingularities	Laurentiu
February 28	Tamanna Chatterjee (Notre Dame)	TBA	Josh
April 4	Sam Grushevsky (Stony Brook)	TBA	Dima

Abstracts

Jakub Koncki

SSM Thom polynomials of multisingularities

Thom polynomials are a tool used for understanding the geometry of singular loci of maps. To a singularity germ \eta we associate a polynomial in infinitely many variables. Upon substituting these variables with the Chern classes of the relative tangent bundle of a stable map, we obtain the fundamental class of the \eta-singular loci of the given map. Thom polynomials have several generalizations, including extension to multisingularities, and polynomials that compute other cohomological properties of the singular loci, such as the Segre-Schwartz-MacPherson class.

In the talk, I will review these concepts and focus on the SSM-Thom polynomials of multisingularities. I will present a structure theorem for them that generalizes earlier results of Kazarian.

The talk is based on a joint project with R. Rimányi.