The seminar meets on selected Fridays 4:00-5:00 PM at the CUNY Graduate Center, room 4214.03 (math thesis room). The CUNY Graduate Center is located at 365 Fifth Avenue, New York, NY 10016.
Organizers:
Laura Ghezzi, New York City College of Technology and the Graduate Center (CUNY), laura.ghezzi58@citytech.cuny.edu
Hans Schoutens, New York City College of Technology and the Graduate Center (CUNY), hschoutens@citytech.cuny.edu
Fei Ye, Queensborough Community College and the Graduate Center (CUNY), feye@qcc.cuny.edu
Spring 2026 dates: February 13, February 27, March 13, April 17, May 8.
February 13, 2026 4-5 PM GC 4214.03
Speaker: Wanchun (Rosie) Shen, Harvard University
Title: Higher Du Bois singularities and K-regularity
Abstract: We explain how recent progress in higher Du Bois singularities leads to new results about K-regularity, a notion that measures the homotopy invariance of algebraic K-theory.
February 27, 2026 4-5 PM GC 4214.03
Speaker: Valeriy Sergeev, CUNY Graduate Center
Title: Bertini Theorems for singularities in positive characteristic
Abstract: We will discuss Bertini Theorems for various singularities both in characteristic 0 and in positive characteristic. We will focus on the case of weakly normal singularities in positive characteristic and their relations with F-singularities.
March 13, 2026 4-5 PM GC 4214.03
Speaker: Ben Blum-Smith, Johns Hopkins University
Title: Generic orbits, normal bases, generation degree for fields of rational invariants
Abstract: Let G be a finite group acting faithfully on a vector space V over a field k. The field Noether number is the minimum degree d such that the invariant polynomials of degree ≤ d generate the field k(V)^G of rational invariants. Researchers have begun to study this quantity as part of the longstanding program on degree bounds in invariant theory, and also motivated by an application to signal processing.
The spanning degree is the minimum degree D such that the (not-necessarily-invariant) polynomials of degree ≤ D span the field k(V) of rational functions as a vector space over k(V)^G. This quantity is related to various goals in representation theory, such as identifying which tensor powers of V are needed to collect every irreducible representation of G.
In this talk, we show that, provided the characteristic of k is coprime with the order of G, these two quantities are always related by the inequality d ≤ 2D + 1, and this is sharp. The proof involves Gröbner bases, the Normal Basis Theorem from Galois theory, and the representation theory of finite groups. The argument also relates both d and D to the degree (as a variety) of a generic orbit of G on V. This is joint work with Harm Derksen.
April 17, 2026 4-5 PM GC 4214.03
Speaker: TBA
Title: TBA
Abstract: TBA
May 8, 2026 4-5 PM GC 4214.03
Speaker: TBA
Title: TBA
Abstract: TBA