6 problems

Let $(f,G\rtimes S)$ and $(\widetilde{f},\widetilde{G}\rtimes S)$ be BHHT-dual pairs, where the permutation group $S$ satisfies the parity condition (PC). Let…

Let $w\in\mathbb{C}[x_1,\ldots,x_n]$ be an invertible polynomial, and let $w^\vee$ be the invertible polynomial defined by the transpose of the exponent matrix of $w$. Write…

Let $\mathbf{w}$ and $\check{\mathbf{w}}$ be a pair of invertible polynomials, let $\Gamma_{\mathbf{w}}$ be the maximal symmetry group of $\mathbf{w}$, and let…

Let $w\in \mathbf{k}[x_1,\dots,x_n]$ be an invertible polynomial, and consider the hypersurface $\{w=0\}$ in $\mathbb{A}_{\mathbf{k}}^n$. Let $L_w$ be the maximal grading group, an…

Orlov's block conjecture. This category admits a full strongly exceptional collection consisting of at most $n+1$ blocks, where each block consists of pairwise orthogonal objects.…

Let $f$) be an invertible polynomial in $n$ variables, let $S$ be a subgroup of the permutation group $S_n$ preserving $f$ and satisfying the parity condition (PC), and let $G$ be…