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