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Discrete CATS Seminar

Date:
Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
Joseph Cummings, U Kentucky

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.

Event Series: