Speaker: Gordon Kirby

Title: Posets, Shellability, and the Bruhat order

Abstract: This talk aims to explore some basic poset topology and combinatorial restrictions on edge labelings of the Hasse diagram in order to define Cohen-Macaulay posets. Specifically we will discuss shellability and EL-shellability. We will also look at the Bruhat order on the symmetric group for some examples. The goal is to convey some appreciation for the interactions of combinatorics, algebraic topology and commutative algebra.