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, May 15.
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: Anda Tenie, Harvard University
Title: Global smoothing of singular Fano and Calabi-Yau varieties
Abstract: When studying deformations of singular varieties, a fundamental question is whether they admit smoothings. In this talk, I will describe new results in this direction for higher-dimensional singular Fano and Calabi-Yau varieties with Du Bois isolated complete intersection singularities. We obtain smoothing criteria by imposing local conditions on the singularities, expressed in terms of the recently introduced notions of higher rational and higher Du Bois singularities. In the Calabi-Yau case, one must also impose a global condition, which we formulate in terms of the Hodge-Du Bois numbers of the variety. Our results recover and extend various theorems of Friedman, Namikawa, Namikawa-Steenbrink, Gross, and Friedman-Laza.
May 8, 2026 4-5 PM GC 4214.03
Speaker: Anh Duc Vo, Columbia University
Title: Generic vanishing for singular varieties
Abstract: We establish appropriate generic vanishing theorems for singular varieties, generalizing the well-known generic vanishing theorem by Green and Lazarsfeld. Our theorem also explains the counterexample of Hacon and Kovács to a “naive” generalization.
May 15, 2026 4-5 PM GC 4214.03
Speaker: Sheng-Li Tan, East China Normal University, Shanghai
Title: Modular Invariants in Algebraic Geometry and Their Applications
Abstract: Riemann’s classification theory of algebraic curves is a cornerstone of modern mathematics. The moduli spaces of curves provide modular invariants for families of curves. Such invariants are important tools for studying Diophantine problems in number theory. In recent years, modular invariants have also been applied to differential equations and cubic equations. In this talk, I will review the history, explain some recent developments, and introduce some open problems in this area.