7 problems

Let $N$ and $k$ range over positive integers, and let $\mathcal{C}(\mathfrak{sl}_N,k)$ denote the corresponding categories. Let $\mathcal{A}$ be the set of all non-pointed étale al…

For each $n\in{\bf N}$, let $M_n$ be a random planar map sampled as in the planar-map model above, and embed it into $\mathbbm S^2$ or a subset of $\mathbbm C$ by a discrete confor…

Let $N\in\mathbb{Z}_{>0}$ and let $k=-N+p/n$ be admissible. Write $\pi$ for a rank-one Heisenberg vertex algebra, and set $L_\bullet(\mathfrak{sl}_i)=\mathbb{C}$ for $i=0,1$. Excep…

The conjecture on the image of the conformal embedding map. The image of the homomorphism $\Phi$ is isomorphic to

Let a random planar map with $n$ vertices or faces be mapped by a discrete conformal embedding to points in the unit disk, and assign mass $1/n$ to each embedded vertex or face, th…

Let $n,m$ be positive integers with $n\geq 2$. Define $\mathcal{W}_{n,m}$ as the quantum Hamiltonian reduction of $V_k(\mathfrak{sl}_{n+m})$ at the level satisfying … Here the redu…

Let $\mathfrak k\hookrightarrow \mathfrak g$ be an embedding of a reductive subalgebra into a semisimple finite-dimensional complex Lie algebra. The embedding is conformal when the…