Abstract:
Let $\operatorname{Mat}_{n \times n}(\mathbb C)$ be the affine space of $n \times n$ complex matrices with coordinate ring $\mathbb C[\mathbf{x}_{n\times n}]$. We define graded quotients of $\mathbb C[\mathbf{x}_{n\times n}]$ where each quotient ring carries a group action. These quotient rings are obtained by applying the orbit harmonics method to matrix loci corresponding to the permutation matrix group $\mathfrak S_n$, the colored permutation matrix group $\mathfrak S_{n,r}$, the collection of all involutions in $\mathfrak S_n$, and the conjugacy class of fixed point free involutions in $\mathfrak S_n$. In each case, we explore how the algebraic properties of these quotient rings are governed by the combinatorial properties of the matrix loci. Based on joint work with Yichen Ma, Brendon Rhoades, and Hai Zhu.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974