Algebra Seminar: Strong test ideals of Stanley-Reisner rings

When:
October 5, 2017 @ 11:00 am – 12:15 pm
2017-10-05T11:00:00-04:00
2017-10-05T12:15:00-04:00
Where:
M&S Seminar Room 1441
25 Park Pl NE
Atlanta, GA 30303
USA
Contact:
Florian Enescu

Title
Strong test ideals of Stanley-Reisner rings

Speaker
Irina Ilioaea, Department of Mathematics and Statistics, Georgia State University

Abstract
The main purpose of this talk is to show how we can determine strong test ideals of Stanley-Reisner rings using an algorithm of Katzman and Schwede. The main result of the talk states that the number of generators of the test ideal associated to pairs of Stanley-Reisner rings and linear maps is actually the number of facets of the simplicial complex associated to the Stanley-Reisner ideal. An important consequence of this result is that every element belonging to the tight closure of a square-free monomial ideal I satisfies an integral dependence equation of degree equal to the number of facets of the simplicial complex associated to the ideal I over I.