For recordings of virtual talks see
Fall 2023 talks
October 13
Speaker: Andrew Stout, BMCC (CUNY)
Title: Jet Schemes: From Local to Global Deformations
Abstract: We consider jet schemes of flat deformations over simple linear fat points. It is shown that, for locally complete intersection varieties, these spaces can be viewed as global flat deformations over affine n space of the classical jet scheme of order n. This has natural implications for defining a motivic volume and developing an analogue of the motivic Milnor fiber. These results were obtained by further developing previous work done by the speaker on Auto Arc Spaces (a type of generalized jet scheme). Auto Arc Spaces were originally introduced into the literature by Prof. Hans Schoutens.
Preprint: https://arxiv.org/abs/2309.14656
October 27
Speaker: Han-Bom Moon, Fordham University
Title: Derived category of moduli space of vector bundles
Abstract: The derived category of moduli spaces of vector bundles on a curve is expected to be decomposed into the derived categories of symmetric products of the base curve. I will explain the current status of knowledge and how one can show that the derived category of the symmetric product of the base curve can be embedded into the derived category of the moduli space. This is joint work with Kyoung-Seog Lee.
November 10
Speaker: Valeriy Sergeev
Title: F-Rational Rings and Rational Singularities
Abstract: Rational singularities are an important class of singularities, closely related to many areas of algebraic geometry, including geometric invariant theory and the minimal model program. Rational singularities are defined using desingularizations. Despite this fact, rational singularities are closely related to singularities defined in terms of Frobenius map in prime characteristic, where existence of desingularizations is still an open question. We will discus results of Smith and Schoutens that explore this relationship.
December 1
Speaker: Uyen (Enni) Le, West Virginia University
Title: Remarks on a conjecture of Huneke and Wiegand
Abstract: This talk centers around the Huneke-Wiegand Conjecture, which has been a long-standing problem. Unlike vector spaces over a field, not all modules over a ring have a basis. Using an operation known as the tensor product, the Huneke-Wiegand Conjecture seeks conditions on a module M with rank over a one-dimensional local ring such that M has a basis (i.e., M is free).
Building upon the foundational work of Huneke and R. Wiegand in 1994, and O. Celikbas in 2020, we provide affirmative results for this conjecture in specific cases. In particular, we establish results for 2-periodic modules over local rings (joint work with Olgur Celikbas, Hiroki Matsui, and Arash Sadeghi), as well as 4-periodic modules over Gorenstein rings.
Note: This talk will be virtual on zoom
https://us02web.zoom.us/j/81549606766?pwd=WGsrK3k4dVpjM0pGbDZzNGFPWFVNdz09
Meeting ID: 815 4960 6766
Passcode: 489570
