15 problems

Let $E_0$ and $E_1$ be the objects appearing in the surgery-formula construction, and let $\operatorname{End}_{w\mathrm{Fil}}(\beta_0^{E_0}\oplus\beta_1^{E_1})$ denote the endomorp…

Let ${\mathrm{K}}_m^n$ be the extended Khovanov arc algebra indexed by $m$ and $n$, and let $\operatorname{HH}^2_{i-2}({\mathrm{K}}_m^n,${mathrm{K}}m^n)…

Suppose $(X,\omega)$ and $\mathcal D$ are as in the beginning of the introduction, and let $L\subset X\setminus\mathcal D$ be a relatively spin compact Lagrangian submanifold. Let…

Let $W$ be a Coxeter group with realization $V$ over $\mathbb{C}$, and let $\mathcal{C}(W)$ denote the corresponding Soergel Hecke category. Let $\operatorname{Tr}$ be its universa…

Let $M$ be an orientable $N$-dimensional $k$-connected compact manifold, with $\dim H^{k+1}(M)=1$. Let $l\geq 3$ and assume … An $A_\infty$-minimal model of $\Omega^*(M)$ is a mini…

Let $(X,[?]$

Let $\Pi_n$ be the $n$-dimensional pair of pants, let $L_I$ be the relevant objects, and consider the algebra $\bigoplus_{I,J}HW^*(L_I,L_J)$. Assume its $A_\infty$-structure is com…

Infinity-contraction algebra reconstruction conjecture. The completions of the stalks at $p$ and $q$ are isomorphic if and only if $A^\infty_{con}$ and $B^\infty_{con}$ are derived…

Open quantum Kirwan map conjecture. Counting affine vortices over the upper half-plane $\mathbb H$ defines an $A_\infty$ morphism

Let $\mathbb{K}$ be a ground field of characteristic zero, let $\Gamma$ be a tree of type $E_6$, $E_7$, or $E_8$, and let $A_\Gamma$ be the corresponding zigzag algebra. Exceptiona…

Let $S$ be the underlying scheme, and let $\mathcal{B}$ be a sheaf of $\mathbb{Z}$-graded differential-graded $\mathcal{O}_S$-algebras and $\mathcal{A}$ a sheaf of $\mathbb{Z}$-gra…

Unitality–homotopy unitality equivalence. An $A_\infty$-morphism is unital if and only if it admits a homotopy unital structure; equivalently, any unital $A_\infty$-morphism admits…

Let $\SB$ be an exceptional block, and let $A_\SB$ be the associated $A_\infty$ algebra. One-generation conjecture. The algebra $A_\SB$ is one-generated as an $A_\infty$ algebra, a…

Let $E_m^n$ denote the Ext algebra considered in the paper, equipped with its induced algebra structure and viewed as a differential graded algebra up to quasi-isomorphism. Non-for…

Let $X$ be a finite-dimensional vector space, let $A=\wedge(X)=\mathrm S(X[-1])$ with generators of degree $1$, and let $B=\mathrm S(X^*)$ concentrated in degree $0$. Let $K$ be th…