##### Department of Mathematics,

University of California San Diego

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### Math 296 - Graduate Student Colloquium

## Brendon Rhoades

#### UCSD

## The mysteries of Chern plethysm

##### Abstract:

Symmetric functions are highly ubiquitous in algebraic combinatorics, with connections to the representation theory of $GL_n$ and $S_n$, the geometry of Grassmannians, and more. There is a classical way to 'compose' symmetric functions called plethysm which has a nice representation-theoretic interpretation. We will describe a related operation called Chern plethysm which has inputs given by a symmetric function F and a vector bundle E and outputs a symmetric polynomial. Chern plethysm provides numerous Schur-positivity results, indicating a representation-theoretic connection, but finding this connection remains an open problem. Joint with Sara Billey and Vasu Tewari.

### January 9, 2020

### 12:00 PM

### AP&M 6402

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