##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Adrian Garsia

#### UCSD

## Hall Littlewood Operators in Theory of Parking Functions and Diagonal Harmonics

##### Abstract:

This is the first of a series of lectures covering recent progress on the Shuffle conjecture. We will start with the work of Haglund-Morse-Zabrocki leading to the compositional refinement of the Shuffle conjecture. Then give a detailed presentation of the joint work with Guoce Xin and Mike Zabrocki leading to the compositional refinement of the q,t-Catalan and Schroeder results. These lectures will cover the symmetric function side of the result. The combinatorial side is work of Angela Hicks. Her results consist of two surprising Parking function bijections refining the q,t-Catalan and Schroeder recursion that will be presented by her sometime later this year to complete the proof of these two special cases of the Haglund-Morse-Zabrocki conjectures.

### January 26, 2010

### 3:00 PM

### AP&M 7321

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