##### Department of Mathematics,

University of California San Diego

****************************

### Recruitment (Combinatorics)

## Alexander Yong

#### UC Berkeley

## When is a Schubert variety Gorenstein?

##### Abstract:

Schubert varieties are classical objects of study in algebraic geometry; their study often reduces to easy-to-state combinatorial questions.Gorensteinness is a well-known measure of the "pathology" of the singularities of an algebraic variety. Gorensteinness is a condition that is logically weaker than smoothness but stronger than Cohen-Macaulayness. We present a non-recursive, combinatorial characterization of which Schubert varieties in the flag variety are Gorenstein. Our answer is in terms of generalized permutation pattern avoidance conditions. I'll explain the algebraic geometric and representation (Borel-Weil) theoretic applications of this work. I will also describe further combinatorial questions. \vskip .1in \noindent This is a joint project with Alexander Woo, see math.AG/0409490.

Host: Jeff Remmel

### January 25, 2005

### 3:00 PM

### AP&M 7321

****************************