13 problems

Let $\mathbb{X}$ be an $\mathbb{A}_n$-schober, and let $\mathbb{X}_{11 \cdots 1}$ denote its underlying stable $\infty$-category. Coherent braid-action conjecture. $\mathbb{X}$ def…

Let $G(\mathbb{S},n)$ be the relative graded Brauer graph algebra associated with the weighted surface data $(\mathbb{S},n)$, and let…

The A-model concerns the Fukaya-type 2-category of boundary conditions for a 3-dimensional A-model associated with a 3d $\mathcal N=4$ theory. Inspired by analogous theorems for Fu…

Let $A$ be a configuration of points, let $\mathfrak{S}\in\operatorname{Schob}(\mathbb{C},A)$, and let $\mathfrak{g}_A(\mathfrak{S})$ be the associated $L_\infty$-algebra. For a tr…

Let $A$ be the configuration of points defining the schober, let $\mathfrak{S}\in\operatorname{Schob}(\mathbb{C},A)$, and let $({\tt{R}}^\bullet_{ij},q)$ be the $(i,j)$th infrared…

Let $M$ be the Fukaya-Seidel monad and $R$ the infrared monad, with components $M_{ij}$ and $R_{ij}$, respectively. Infrared monad deformation conjecture. Each component $M_{ij}$ o…

Let $\mathcal{P}$ be a perverse schober on $\mathbb{C}$, let $\mathcal{P}_{[0,1)}$ denote its local category near the origin, and let $\mathcal{P}_{\mathbb{C}^\times}$ denote the c…

Sanda–Shamoto's Dubrovin conjecture. There exists an irregular perverse schober whose nearby cycle is $D^b(X)$ and whose Hochschild decategorification gives Stokes data that is the…

Let $Y_{-C}\xleftarrow{\,l_{0,-C}\,}Y_0\xrightarrow{\,l_{0,C}\,}Y_C$ be the Schubert flop diagram for a one-dimensional face $C$ in the remaining case described in the paper. The m…

Let $\mathcal{C}$ be the poset of faces and let $X_C$ be the associated varieties, with the derived categories $D^b(X_C)$ forming the corresponding diagram. Homotopy-colimit conjec…

Let $Z$ be the variety introduced earlier in the construction, let $X_0$ be the variety associated with the zero face, and for each chamber indexed by $w$ let $X_w$ be the correspo…

Let $Z^{\rm core}$ be the core produced by the reduction process, whose flat structure determines a cubic differential and a cyclic $3$-fold spectral covering. Let the perverse Sch…

Schober reconstruction conjecture. The Schober $\mathfrak{S}$, together with a stability structure on it, can be recovered from the family