Events for 02/08/2022 from all calendars

Colloquium - Jay Yang

Time: 4:00PM - 5:00PM

Location: ZOOM

Speaker: Jay Yang, McMaster University

Description:
Title: Homological and Probablistic Techniques in Commutative Algebra
Abstract: Syzygies and free resolutions are foundational topics for modern Commutative Algebra. They provide invariants that encode the algebraic and geometric structure of modules. In this vein, I will discuss work on random monomial ideals and virtual resolutions which blends techniques from probability, combinatorics, and commutative algebra.
On the probabilistic side, my work on random monomial ideals has produced strong heuristics for the behavior of families of ideals. In particular I consider asymptotic syzygies in the flavor of Ein and Lazarsfeld as well as the question of characteristic dependence of Betti numbers for modules. With virtual resolutions, which are a variation of free resolutions which exhibit better behavior in the multigraded setting, I prove bounds on their lengths and consider the case of virtually Cohen--Macaulay modules.