## Algebra and Combinatorics Seminar

**Date:** November 1, 2019

**Time:** 3:00PM - 3:50PM

**Location:** BLOC 628

**Speaker:** Byeongsu Yu, Texas A&M University

**Title:** *Generalized Ishida Complex*

**Abstract:** Today, we will discuss the generalized Ishida complex. Masa-nori Ishida devised the Ishida complex to calculate local cohomology over the maximal ideal of a normal affine semigroup ring. We generalized this to calculate the local cohomology over all monomial supporting ideal. First of all, we will recall the definition of local cohomology and Čech Complex method. Then, we will investigate the properties of an affine monoid. Actually, an affine monoid can be viewed as a ring or as a polyhedral complex. A combination of these viewpoints allows us to have a cochain complex. This cochain complex comes from the polyhedral cone structure of the monomial ideal. Lastly, we will sketch to prove a statement that Generalized Ishida's complex calculates the local cohomology on affine semigroup ring over any monomial supporting ideal.