##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Adriano Garsia

#### UCSD

## The two sides of the Extended Shuffle Conjectures

##### Abstract:

Recent work of Eugene Gorsky and Andrei Negut have put the finishing touches of what may be viewed as the symmetric function side of the Extended Shuffle conjectures. Their work, together with Hikita's construction of the combinatorial side combine into a truly remarkable family of conjectures which beautifully extend the classical Shuffle conjecture. These developments have opened up a vast research area of Algebraic Combinatorics considerably enlarging classical symmetric function theory as well as the Theory of Parking functions created by Computer Scientists. This talk is an elementary introduction to this new research area.

### October 8, 2013

### 4:00 PM

### AP&M 7321

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