## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Serre Condition $S_r$ for Simplicial Complexes

Seminar | October 10 | 3:45-4:45 p.m. | 939 Evans Hall

Brent Holmes, University of Kansas

Department of Mathematics

For a fixed integer $r$, Serre's condition $S_r$ is a condition on the depth of a ring at various localizations. It can be viewed as a weakening of the Cohen-Macaulay condition. In this talk, we focus on Serre's condition for Stanley-Reisner rings. The first main topic will be the relationship between Serre's $S_2$ condition and Hirsch type bounds on the diameter of the dual graph. The second topic is some homological properties of Stanley-Reisner rings with $S_r$ condition using higher nerves.

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