8 problems

Correspondence conjecture. The table below, obtained using the preceding information together with heuristics, gives the correct correspondence between module categories and modula…

Let $g_{2n}$ denote the coefficients appearing in the higher-dimensional partition functions, indexed by the positive integer $k$. Periodicity conjecture. The coefficients $g_{2n}$…

Fix $t=e^{2i\pi/p}$, where $p$ is the Coxeter number of the Coxeter–Dynkin diagram, and let $\rho_{hh'}$ be an irreducible representation occurring in the decomposition of the Hilb…

Monotonicity conjecture. For all $\theta\in\left[\frac{\pi}{2},1.9\right]$, the first function is decreasing on $[0,0.5]$, and for all $\theta\in\left[1.9,\frac{2\pi}{3}\right]$, t…

Let $\mathbf{c}$ be the central charge of the gravity theory, and let $\mathbf{c}_{\rm crit}$ be the critical central charge determined by the given boundary chiral algebra. The Po…

Let $G$ be a compact, connected, simply-connected Lie group with an automorphism $\omega$. Let $\mathcal{N}^{GG}_\lambda$ be the matrices constructed from the $\omega$-fixed points…

Let $G$ be a simply-connected, compact, connected Lie group, let $k$ be a level, and let $M_k(G)$ be the integer appearing in the twisted nonequivariant groups $^{\kappa}K_*(G)$, w…

Kreuzer–Schellekens' conjecture. All simple current physical invariants can be obtained as orbifolds of the diagonal physical invariant by a subgroup of the centre; equivalently, t…