##### Department of Mathematics,

University of California San Diego

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### Combinatorics Seminar (Math 269)

## Brendon Rhoades

#### UCSD

## The superspace coinvariant ring

##### Abstract:

The classical coinvariant ring $R_n$ is obtained from the polynomial ring $\mathbb{C}[x_1, \dots, x_n]$ by quotienting by the ideal $I_n$ generated by symmetric polynomials with vanishing constant terms. The {\em superspace coinvariant ring} $SR_n$ is obtained analogously, but starting with the ring $\Omega_n$ of regular differential forms on $n$-space. We describe the bigraded Hilbert series of $SR_n$ in terms of ordered set partitions and give an `operator theorem' which describes the harmonic space attached to $SR_n$. This proves conjectures of N. Bergeron, Li, Machacek, Sulzgruber, Swanson, Wallach, and Zabrocki. This talk is based on joint work with Andy Wilson.

### May 23, 2023

### 4:00 PM

APM 6402 (Halkin Room)

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