UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 11, 2020

939 Evans Hall

3:45PM: Hilbert schemes and link homology

Eugene Gorsky

Khovanov and Rozansky defined a link homology theory using Soergel bimodules. This invariant has a lot of interesting properties, but it is notoriously hard to compute. I will define it in terms of discuss recent progress in understanding Khovanov-Rozansky homology and its surprising relation to algebraic geometry of the Hilbert scheme of points on the plane. In particular, I will compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme. All notions will be introduced in the talk, no preliminary knowledge is required. The talk is based on joint works with Matt Hogancamp, Andrei Negut and Jacob Rasmussen.

5:00PM: An overview of Bertini-type theorems

Lauren Heller

A classical theorem of Bertini gives conditions under which a general member of a linear system of divisors is smooth. I will discuss this theorem and several variations of it, including generalizations by Zariski and Flenner and a recent paper of Ghosh and Krishna.

Return to Seminar Listing