##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Alex Postnikov

#### Massachusetts Institute of Technology

## Towards general Schur positivity and higher saturation

##### Abstract:

We prove Schur positivity conjectures due to Fomin-Fulton-Li-Poon and Okounkov and give several related results. We show that Schur polynomials satisfy an interesting Schur-log-concavity property. We discuss a "higher Klyachko problem" about inequalities between Littlewood-Richardson coefficients and formulate a general Schur positivity conjecture involving certain mysterious convex polytopes. The talk is based on a joint work with Thomas Lam and Pavlo Pylyavskyy.

Host: Adriano Garsia

### May 9, 2006

### 4:00 PM

### AP&M 7321

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