8 problems

Let ${\cal C}$ be an $A_{\infty}$-category such that $HH^1({\cal C})$ is abelian and the connected automorphism group $G_{\cal C}=Aut^0({\cal C})$ is a finite-dimensional commutati…

Let $\mathbb{T}^n_\theta$ be the quantum torus, let $\Delta$ be its flat Laplacian, let $q>0$, set $r=2nq^{-1}$, and suppose that either $r\neq 1$ and $r'=\max(r,1)$, or $r=1<r'$.…

Let $L$ be a link, let $\mathsf{H}_q(L)$ be its HOMFLYPT difference module, let $[L]$ be its distinguished link class, and let $\mathsf{ev}\colon \mathsf{H}(L)\to \mathcal{F}_r$ be…

Let $U$ be the quantum group, $Z$ its center, $U_0$ its Cartan subalgebra, $F_l(U)$ the relevant left fraction algebra, and let $\mathcal O_q[G/H]$ and $T$ be the quantum homogeneo…

Endpoint complex interpolation conjecture.

Kontsevich–Soibelman integration-map conjecture. There exists an $L$-graded $\Lambda$-algebra homomorphism

Absence of poles conjecture. For any $3d$ Calabi–Yau category with a stability condition and any strict sector $V$, the automorphism $x\mapsto A_{V,q}xA_{V,q}^{-1}$ preserves the s…

Let ${}^{\bullet}\wp^{\mathrm{nc}}_{\mu,\theta}$ and ${}^{\bullet}\wp'_{\mu,\theta}$ be the quantum nonstandard Weierstrass function and its derivative, and let…