6 problems

Let $M$ be a combinatorial map and $W$ a choice of loop weights, and write $Z_{M,W}$ for the associated loop-model correlation function. Assume the critical limit exists. The corre…

Let $\mathcal{S}_{r_0}$ denote the relevant channel spectrum indexed by the smallest first Kac index $r_0$, and let $\mathcal{M}_{0,4}(r_i\mid\sigma_s,\sigma_t,\sigma_u)$ be the se…

Let an $n$-point function of diagonal and non-diagonal fields lie on a Riemann surface of genus $g$. In each channel, consider conformal-bootstrap spectra containing all allowed no…

Consider an $n$-point function of diagonal and non-diagonal fields on a Riemann surface of genus $g$. Let $\mathcal{M}^c_{g,n}(r_i)$ denote the set of weakly connected maps with th…

Let $\mathcal{M}_{0,4}(r_1,r_2,r_3,r_4)$ be the set of maps with the specified vertex data, and order signatures componentwise: $sigma ot greater than or equal tosigma'$ when…

In two-dimensional statistical physics, correlation functions of the $O(N)$ and Potts models can be expressed as sums over configurations of non-intersecting loops. For a large cla…