##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Adriano Garsia

#### UCSD

## The Shuffle Conjecture and the Polynomials of Angela Hicks

##### Abstract:

The Shuffle Conjecture gives a Combinatorial setting to the bi-graded Frobenius Characteristic of the Diagonal Harmonic Module of $S_n$. We report here on the progress in joint work with Angela Hicks in a three year effort to prove this conjecture. Angela Hicks reduced a combinatorial side of the problem to proving a deceptively simple property of a remarkable family of polynomials in a single variable $x$ with coefficients polynomials in $N[q]$. In this lecture and possibly following ones we describe what remains to be done to resolve this decade old Algebraic Combinatorial problem.

### January 31, 2012

### 3:00 PM

### AP&M 7321

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