Speaker:  Joseph Cummings, U Kentucky

Title:  Cohen-Macaulay Stanley-Reisner Rings

Abstract:

It turns out that in order to solve many purely combinatorial problems relating to simplicial complexes, one needs to study algebraic properties of its Stanley-Reisner ring. For example, we will show the Cohen-Macaulay condition gives us sharp bounds on the complex’s $h$-vector. We will also discuss Reisner’s criterion which gives an equivalent combinatorial criterion for Cohen-Macaulyness, and time permitting, Stanley’s upper bound theorem for simplicial spheres.