Algebra and Algebraic Geometry Seminar Fall 2025

The seminar normally meets 2:30-3:30pm on Fridays, in the room Van Vleck B321. You can find the old schedules of the seminar here.

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Fall 2025 Schedule

date	speaker	title	host/link to talk
September 19	reserved		Jose/Andrei
September 26	Shuddhodan Kadattur Vasudevan(Notre Dame)	Perverse filtrations via Brylinski-Radon transformations	Botong
October 24	Shamgar Gurevich	A look at representations of SL(2,F_q) through the lens of size	local
October 31	Thomas Hameister(Boston College)	TBA	Dima/Josh

Abstracts

Shuddhodan Kadattur Vasudevan

Perverse filtrations via Brylinski-Radon transformations

In 2010, de Cataldo-Miglorini showed how to compute the perverse filtration on the cohomology of an affine variety with values in a constructible sheaf using generic flags. In this talk, I shall introduce the Brylinski-Radon transformation, discuss its properties and derive consequences for the perverse filtration. Time permitting we shall also discuss some arithmetic applications of our results. This is joint work with Ankit Rai.

Shamgar Gurevich

A look at representations of SL(2,F_q) through the lens of size

Harmonic analysis studies functions on the real line by expanding them as sums of frequencies (exponentials), and studying how each term contributes to the overall sum. In many applications, such as speech recognition, only low frequencies contribute meaningfully.

There is a philosophy, developed by Roger Howe (Yale) over the last 50 years, that this should apply in many other situations.

In a joint work with Howe, we have introduced such a theory for finite classical groups. A class function on a group can be written as a linear combination of irreducible characters, and we define a notion of “frequency" (aka size) for such objects. This provides a new way of analyzing the function.

In my talk, I would like to “sell" you on this approach in the first non-trivial example of the group SL(2,F_q) of 2x2 matrices with entries in the finite field F_q and determinant equal to one.

The talk should be accessible to anybody who took a good course in linear algebra.

Thomas Hameister

TBA