##### Department of Mathematics,

University of California San Diego

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### Math 264 - Combinatorics

## Allen Knutson

#### University of California at Berkeley

## Gluing Young tableaux into a ball

##### Abstract:

Young tableaux, beloved of combinatorialists, tolerated by representation theorists and geometers, seem at first glance to be an unruly combinatorial set. I'll define a simplicial complex in which they index the facets, and slightly more general objects (Buch's ``set-valued tableaux'') label the other interior faces. The theorem that says we're on a right track: This simplicial complex is homeomorphic to a ball. I'll explain why this is surprising, useful, and shows why Buch didn't discover the exterior faces too. Finally, I'll explain how algebraic geometry forced these definitions on us (or, ``How I made my peace with Young tableaux''). This work is joint with Ezra Miller and Alex Yong.

Host: Jeff Remmel

### November 30, 2004

### 3:00 PM

### AP&M 7321

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