University of Minnesota Combinatorics Seminar: 2020-2021

Date: 10/02/2020

Speaker: Jay Yang

Random Flag Complexes and Torsion in Syzygies of Random Monomial Ideals
In our paper Random Flag Complexes and Asymptotic Syzygies, Daniel Erman and I constructed a model of a random monomial ideal, and showed that the Betti tables for the ideals in this model exhibited asymptotic behavior reminiscent of the Veronese module. This inspired recent work with Daniel Erman and Caitlyn Booms showing that Stanley--Reisner ideals corresponding to random flag complexes almost always have Betti tables that depend on characteristic. We use this to offer a heuristic on when to expect that the syzygies of the Veronese should depend on characteristic.

Random Flag Complexes and Torsion in Syzygies of Random Monomial Ideals

In our paper Random Flag Complexes and Asymptotic Syzygies, Daniel Erman and I constructed a model of a random monomial ideal, and showed that the Betti tables for the ideals in this model exhibited asymptotic behavior reminiscent of the Veronese module. This inspired recent work with Daniel Erman and Caitlyn Booms showing that Stanley--Reisner ideals corresponding to random flag complexes almost always have Betti tables that depend on characteristic. We use this to offer a heuristic on when to expect that the syzygies of the Veronese should depend on characteristic.