5 problems

Let $f$ be the series entering the Virasoro fusion kernel, and let $\beta^2$ approach a rational value. Rational-limit conjecture. The limit of $f$ as $\beta^2$ tends to a rational…

Let $c<1$ and let the physical fusion kernel denote the fusion kernel relevant to the physical regime of Liouville theory at central charge $c$. Ribault and Tsiares' conjecture. Th…

Let $b^2 \notin \mathbb Q$ and suppose that $b^2$ is not a Liouville number: there exist $m,q_0\in\mathbb N$ such that, for every $(p,q)\in\mathbb Z\times\mathbb Z_{\geq q_0}$, … L…

Let $c$ be the central charge of the Virasoro algebra, let $b$ be the parameter related to it by $c=1+6(b+b^{-1})^2$, and let the fusion and modular kernels be functions or distrib…

Let $c$ be the central charge of the Virasoro algebra, let $b$ be the parameter related to it by $c=1+6(b+b^{-1})^2$, and let the fusion and modular kernels be functions or distrib…