15 problems

Let $H_\circ$ be a Hamiltonian whose ground state $G_{\circ,{\bf l}}$ has log-extensive degeneracy, and let $G_{\epsilon,{\bf l}}$ be the strictly less degenerate ground state obta…

Let $k$ be a rational level, and let the formulas referred to as … provide all solutions to the system $(,)$ and conjectures that, when $k$ is rational, they actually give horizont…

The construction produces a flat connection whose horizontal sections solve the associated Knizhnik–Zamolodchikov and singular-vector differential equations. All-horizontal-section…

Let $S$ be a surface with holes, let $S'$ be obtained by cutting $S$ along a simple loop, and let $\gamma_\pm$ be the two new boundary components. Let ${\bf V}_{G,S;\lambda}$ be th…

Let $S$ be a punctured surface, and let $G=SL_m$. The cluster ensemble $({\cal A}_{G,S},{\cal X}_{G,S})$ yields a family of unitary projective representations of the mapping class…

The moduli space ${\cal X}_{G,\widehat S}$ carries a cluster ${\cal X}$-variety structure, and the construction in the paper assigns to $(G,\widehat S)$ an infinite-dimensional uni…

Let $G=\operatorname{PGL}_{n+1}$, let $S$ be a marked surface, and let $c$ be an essential simple closed curve on $S$. Let $S'$ be obtained by cutting $S$ open along $c$, and let…

Tensor-product equivalence conjecture. The map above induces an equivalence of monoidal categories

Let $cmathfrak{g}$ be a complex finite-dimensional simple Lie algebra, let $cell$ be a positive integer, and let $czeta$ be an allowed root of unity defining the modular functor…

Let $\mathfrak{S} = \Sigma \setminus \mathcal{P}$ be a triangulable marked surface, let $\Delta$ be an ideal triangulation, and let $\hbar \in \mathbb{R}_{>0}$. For an essential si…

Let $R^mp_*\mathcal{L}$ be the higher direct image local system associated with the geometric construction in the paper, and let the space of conformal blocks be the corresponding…

Equivalence conjecture. The modular functor induced by $\mathrm{V}'_{\mathcal C}$ is equivalent to Lyubashenko's modular functor.

Let ${\mathfrak g}$ be a Lie algebra, let ${{}^{\rm\scriptscriptstyle L}{\mathfrak g}}$ be its Langlands dual Lie algebra, and let $k$ and $\check{k}$ satisfy … Here $h^{\vee}$ and…

Let $\Sigma$ be a surface, let ${\mathfrak g}$ be a Lie algebra, and let $k$ be a level. Write $\mathcal W_k({\mathfrak g})$ for the W-algebra associated with ${\mathfrak g}$, and…

A unitary rational conformal field theory (RCFT) has a modular functor, and a Chern–Simons–Witten (CSW) theory is labeled by a pair $(G,\lambda)$ with $G$ a compact group and…