8 problems

Let $n,d\ge 3$, let $V$ be a $d$-dimensional vector space, and let $\sigma:\mathbb{Z}\to\{1,2,\dots,d-1\}$ be a generalized signature of period $n$. Set…

Let $V$ be a finite-dimensional vector space over $k$, and write $d=\dim_k(V)$. Let ${\Lambda}^{S^2}_V(m)$ denote the degree-$m$ component of the exterior graded Swiss-Cheese opera…

Let $W$ be a coincidental complex reflection group, let $S(V^*)$ be the symmetric algebra on the dual of its reflection representation, and choose basic invariants $f_1,\ldots,f_n$…

Let $E$ be an exterior algebra over $\mathbb C$ with $n$ generators, let $f,g\in E$ be generic quadratic forms, and let $S$ be the corresponding commutative polynomial ring with ge…

Crucial–Lundqvist–Nevo conjecture. The Hilbert series of $\Lambda(V)/(f,g)$ is

Let $A$ be a finite ordered set, let $\Bbbk$ be a commutative unital ring, and let $\mathbf{Pl}_A$ denote the plactic monoid on $A$. Theorem gives an injective algebra map from the…

Let $E$ be an exterior algebra and let $J\subset E$ be a pure ideal, meaning an ideal generated by products of linear forms. Suppose that $E/J$ satisfies property (): any two disti…

Let $G$ be a finite abelian group, and let $A=\{a_1,\ldots,a_k\}$ and $B=\{b_1,\ldots,b_k\}$ be two $k$-subsets of $G$. Let $K$ be any field containing an element of multiplicative…