46 problems

Let $kge 2$, let $\beta\in \mathfrak{Br}_n$ be a braid, and let $L(\beta)$ denote its link closure. Write $\mathrm{H}_{0|k}(\beta)$ for the homology constructed in the paper and…

Let $V$ be the Milnor fiber under consideration, let $W^\vee$ be its Berglund–Hübsch mirror polynomial, and let $\Gamma^\vee$ be the maximal symmetry group of $W^\vee$, … Write…

Let $W$ be a regular weight system corresponding to an ADE singularity, and let $f$ be a quasi-homogeneous polynomial attached to $W$. Write $D^b_{\mathbb Z}({\mathcal A}_f)$ for t…

Let $W$ be a regular weight system and $f$ be a quasi-homogeneous polynomial attached to $W$. Assume $W$ has a dual regular weight system $W^*=(a^*,b^*,c^*;h)$ in the sense of K. S…

Let $G$ be the group acting in the above setup, and let $a_i$ and $x_i$ be the coefficients and coordinates defining the quadratic potential … Here $\operatorname{MF}$ denotes the…

Let $U$ be a smooth $\mathbb{C}$-scheme and let $\phi\colon U\to\mathbb{C}$ be a regular function. Let $\mathbf{M}\to\mathbf{Crit}(\phi)$ be a $(-1)$-shifted Lagrangian such that…

Let $\mathrm{X}_{1.9}$ and $\mathrm{X}'_{1.9}$ be the hourglass varieties, and for each $i$ let $\mathcal{MF}_{i}(\mathrm{X}_{1.9})$ denote the left orthogonal component of the exc…

Let $W$ be an invertible weighted homogeneous polynomial in $n+1$ variables, let $\check{W}$ be its Berglund–Hübsch transpose polynomial, and let $\Gamma_W$ be the group acting dia…

Cohomological conjecture. For each combinatorially spin Delzant polytope $\triangle$ such that $X_\triangle^\mathbb{R}$ is Fano, we have

Normed Calabi–Yau conjecture. For each Delzant polytope $\triangle$, the $\infty$-trace $\Theta$ on $MF(W_\triangle)$ is a normed Calabi–Yau structure.

Size-2 boundary characterization conjecture. A positive matrix $M$ is on the topological boundary of $\mathcal{M}_{3,2}^{p \times q}$ if and only if any one of the conditions in th…

The 1-trivial-motion conjecture. The set of $1$-trivial motions of size-$k$ psd factorizations of matrices in $\mathcal{M}_{\binom{k+1}{2},k}^{p \times q}$ is equal to…

Berglund–Hübsch homological mirror symmetry conjecture. There exists a derived equivalence between $\mathcal{F}(W,G)$ and $\mathcal{MF}(W^T,G^T)$.

Let $(A,f)$ be a formal smooth commutative algebra of dimension $d<p$ over $\mathbf{k}$, with superpotential $f\in A$. Assume the HKR-type quasi-isomorphisms … and … Under the iden…

Generalized WAX decomposition validity conjecture. A randomly chosen matrix ${\boldsymbol{H}}$ admits WAX decomposition with probability $1$ for the given ${\boldsymbol{A}}$ if

Let $(W,G)$ be an admissible Landau–Ginzburg pair, with $W$ a nondegenerate quasihomogeneous polynomial and $G$ an admissible subgroup of its maximal symmetry group containing the…

Inverse-matrix conjecture. For $1\leq k\leq n$, the entries satisfy

Let $Q_{d53f\mathbb{R}P^2}$ denote the matrix factorization corresponding, under homological mirror symmetry, to the monotone Lagrangian $(\mathbb{R}P^2,b=0)$, and let … Here…

Let $P$ be a regular local ring with algebraically closed residue field and let $f\in P$. Define … where $\operatorname{Sing}(P/f)$ denotes the singular locus of $P/f$. Buchweitz–G…

Let $V_{n,k}$ be the symmetric-square-type Liouville space considered in the paper, equipped with its natural integer grading $\eta_0$, and let $\mathcal{Z}_{n,k}$ be the special f…

Let $A=(a_{ij})$ be an $(n+1)\times(n+1)$ integer matrix with nonzero determinant, and define … Let $\check{{\bf w}}$ be the polynomial associated to $A^T$, let $\Gamma_{\bf w}$ be…

Let $\mathbf{w}$ be an invertible polynomial with admissible symmetry group $\Gamma\subseteq\Gamma_{\mathbf{w}}$, and let $\widecheck{\Gamma}$ be the corresponding dual group. Let…

Let $\mathbf{w}$ be an invertible polynomial with admissible symmetry group $\Gamma\subseteq\Gamma_{\mathbf{w}}$, and let…

Let $f_n$ be the chain-type invertible polynomial, let $S_n$ and $L_{f_n}$ be the associated ring and grading group, and let $\omega_1,\dots,\omega_n$ be positive rational numbers…

Let $(X,f:X\to\mathbb{C})$ be a Landau–Ginzburg Weinstein sector such that $f$ has no critical values outside $0$, and let $F$ be a general fiber of $f$. Let $\mathcal{W}(X,f)$ and…