##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Adriano Garsia

#### UCSD

## A new proof of Haglund's Diagonal Harmonics Hilbert Series Result

##### Abstract:

By a tour de force argument Jim Haglund opened up a new approach to the computation of several Hilbert series formulas for the Diagonal Harmonics and other closely related Sn modules. Recent joint work with Haglund revealed that the same formulas can be obtained by less painful but more sophisticated uses of pre-existing Macdonald Polynomial identities. In this talk we present a variety of new manipulatorial and combinatorial problems that naturally emerge from these new discoveries.

### November 30, 2010

### 3:00 PM

### AP&M 7321

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