9 problems

Let $R$ be the base algebra, let $A$ be a friendly Calabi–Yau $R$-algebra of dimension $3$, let $F$ be a smooth $R$-algebra, and let…

Let $(D,\omega,\xi)$ be the symplectic data used in the universal construction, and let $A$ be a friendly algebra satisfying the stated Calabi–Yau condition. Theorem main(ii) repre…

Acyclic Ext-quiver conjectures. 1. If $A$ is twisted fractionally Calabi–Yau, then $A$ has an acyclic Ext-quiver. 2. If $A$ is $d$-representation-finite, then $A$ has an acyclic Ex…

Let $\mathbb{L}$ be a compact, relatively spin, graded, oriented immersed Lagrangian of dimension $n$ in a symplectic manifold $M$, and let $\mathcal{A}_{\mathbb{L}}$ be its Maurer…

Formality conjecture. If $Q$ is connected and not Dynkin, then

Let $Q$ be a connected non-Dynkin quiver and let $q\in (\mathbb{C}^\times)^{Q_0}$. Write $\Lambda^q(Q)$ for the multiplicative preprojective algebra of $Q$ with parameter $q$. 2-Ca…

Let $M$ be an acyclic compact orientable manifold, let $\pi(M)$ denote its fundamental group, and let $k[\pi(M)]$ be the corresponding group algebra. Circle-bundle superpotential c…

Let $M$ be a $d$-dimensional compact orientable acyclic manifold, and let $k[\pi_1(M)]$ be its fundamental group algebra. Write $\operatorname{HH}_d(k[\pi_1(M)])$ for its degree-…

Let $M$ be an acyclic oriented compact manifold of dimension $d$, and let $k[\pi_1(M)]$ denote its fundamental group algebra. Superpotential conjecture. If $M$ is an acyclic orient…