Sándor Kovács (UW)

Tuesday, November 22, 2022 - 1:45pm

PDL C-38

Pre-seminar

Title: Grothendieck duality and moduli spaces

Abstract: Grothendieck duality is a far reaching and extremely useful generalization of Serre duality. Unfortunately, it is also (or perhaps accordingly) rather technical. My main goal in this talk is to roughly explain the setup, the ingredients, and how one might use this powerful tool in concrete situations. Time permitting I will also talk about moduli spaces of higher dimensional varieties and how these topics are related.

Title: Grothendieck duality and moduli spaces

Abstract: Grothendieck duality is a far reaching and extremely useful generalization of Serre duality. Unfortunately, it is also (or perhaps accordingly) rather technical. My main goal in this talk is to roughly explain the setup, the ingredients, and how one might use this powerful tool in concrete situations. Time permitting I will also talk about moduli spaces of higher dimensional varieties and how these topics are related.

Seminar

Title: Deformations of singularities, KSB stability, and flatness

Abstract: I will talk about several results, joint with Kollár, regarding deformations of singularities relevant for moduli spaces of canonically polarized varieties, and some consequences. A central player of this area is a class of singularities, called Du Bois singularities, whose definition does not seem to belong here, yet they are fundamentally important to the construction and understanding of these moduli spaces.

Title: Deformations of singularities, KSB stability, and flatness

Abstract: I will talk about several results, joint with Kollár, regarding deformations of singularities relevant for moduli spaces of canonically polarized varieties, and some consequences. A central player of this area is a class of singularities, called Du Bois singularities, whose definition does not seem to belong here, yet they are fundamentally important to the construction and understanding of these moduli spaces.