##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics Seminar

## Gabriel Frieden

#### University of Michigan

## Promotion and geometric lifting

##### Abstract:

Many important maps in algebraic combinatorics (the RSK bijection, the Schutzenberger involution, etc.) can be described by piecewise-linear formulas. These formulas can then be ``de-tropicalized,'' or ``lifted,'' to subtraction-free rational functions on an algebraic variety, and certain properties of the combinatorial maps become more transparent in the algebro-geometric setting. I will illustrate how this works in the case of the promotion map on semistandard tableaux of rectangular shape. I will also indicate how promotion can be viewed as the combinatorial manifestation of a symmetry coming from representation theory, and how its geometric lift fits into Berenstein and Kazhdan's theory of geometric crystals.

Host: Brendon Rhoades

### October 31, 2017

### 4:00 PM

### AP&M 7321

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