## Algebra Seminar - Jonathan O'Rourke - Local Cohomology and Degree Complexes

- Calendar
- Mathematics & Statistics

- Date
- 10.08.2019 11:30 am - 12:30 pm

### Description

Speaker: Jonathan O'Rourke (Tulane University)

Title: Local Cohomology and Degree Complexes

Abstract: In recent years, there has been a great deal of interest in algebraic invariants related to the cohomology of R/I, such as depth and (Castelnuovo-Mumford) regularity, for squarefree monomial ideals and their ordinary and symbolic powers. Due to a formula of Takayama, the dimensions of the graded cohomology modules of R/I are directly linked to the dimensions of the homology of simplicial complexes called

degree complexes. I will define degree complexes, discuss their relationship to regularity, and give results I have obtained on the local cohomology of R/I via degree complexes.