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 2025 dates: February 28, March 14, March 28, April 11, April 25, May 9
February 28, 2025 GC 4214.03
Speaker: Andrew Stout, BMCC (CUNY)
Title: Jets of Local Complete Intersection Morphisms
Abstract: I will give the natural conditions for which the enriched Hom functor (the jet operator) induces a local complete intersection (LCI) morphism given a LCI morphism of schemes. This subsumes my previous work on induced flatness. In addition, it turns out that this is the relativized version of well-known results of Mustata which were used by Eisenbud and Frenkel to prove an important generalization of a theorem of Kostant concerning the nilpotent cone of a Lie algebra. This talk will be accessible to a general mathematical audience.
March 14, 2025 GC 4214.03
Speaker: Fanjun Meng, Johns Hopkins University
Title: Wall crossing for moduli of stable pairs
Abstract: Hassett showed that there are natural reduction morphisms between moduli spaces of weighted pointed stable curves when we reduce weights. I will discuss some joint work with Ziquan Zhuang which constructs similar morphisms between moduli of stable pairs in higher dimension.
March 28, 2025 GC 4214.03 3-5 PM
NOTE: We have 2 talks today
3-4 PM
Speaker: Zhijia Zhang, NYU
Title: Equivariant birational geometry of Fano threefolds
Abstract: The notion of G-varieties was introduced by Manin when he studied rationality problems of surfaces over perfect fields in the 1960s. A G-variety is an algebraic variety carrying a generically free regular G-action. There are close connections, as well as drastic differences between birational geometry of G-varieties and that of varieties over non-closed fields. In this talk, I will explain their similarities and differences through our work on equivariant birational geometry of Fano threefolds of large index (e.g., quadrics, cubics, intersections of two quadrics), with an emphasis on their equivariant unirationalities. This is joint work with Yuri Tschinkel and Ivan Cheltsov.
4-5 PM
Speakers: Sylvan Crane (HSAS-Lehman) and Alexis Menenses (MIT)
Title: Invariant fields of Z/pZ and geometry of numbers
Abstract: Based on computational data, Blum-Smith, Garcia, Hidalgo, and Rodriguez recently conjectured that the field of rational invariants of a representation of Z/pZ, is generated by invariant polynomials of degree at most ceil(p / ceil(m/2)), where m is the number of distinct nontrivial isotypic components in the representation.
In this talk, we prove that this bound holds for fixed m and sufficiently high p, if one is willing to relax the requirement to invariant rational (not necessarily polynomial) functions as generators. We also show this statement fails if one replaces p with a not-necessarily-prime natural number n, and we analyze what goes wrong in the proof. We also discuss the question of whether the generators can be taken to be polynomial. In particular, we prove that, for m≥3, there is always at least a transcendence basis of degree at most (p+1)/2 that is polynomial; this is sharp for m=3.
The methods are based on studying Euclidean lattices, using convexity arguments and Minkowski’s geometry of numbers.
This talk is based on joint work with Ben Blum-Smith, Karla Guzman, and Maxine Song-Hurewitz.
April 11, 2025 4:15-5:15 PM, GC C197 (note the change of room and time for this talk).
Speaker: Herwig Hauser, University of Vienna
Title: Nash Modifications – Revisited
Abstract: Soon after Hironaka’s resolution paper from 1964 an
alternative to classical blowups was produced, so-called Nash blowups.
They are of a more geometric origin and gave hope to produce faster or
more conceptual resolutions. Recent counter-examples in dimension 4 have
disproven this.
In the talk, which is for a general audience, we propose a refinement of
Nash modifications (it is different from Yasuda’s proposal of higher
Nash blowups). This is done by transcribing the differential geometric
concept of curvatures to algebraic varieties. These curvatures capture
nicely the behaviour of varieties near singular points and may
eventually serve to reactivate Nash’s approach to the resolution of
singularities.
April 25, 2025 GC 4214.03
Speaker: Saeed Nasseh, Georgia Southern University
Title: TBA
Abstract: TBA
May 9, 2025 GC 4214.03
Speaker: James Myer, CUNY Graduate Center
Title: TBA
Abstract: TBA
