10 problems

Malliavin–Kontsevich–Suhov (MKS) loop measures are natural measures on curves and loops on Riemann surfaces, characterized by conformal restriction covariance and formulated using…

Let $W_{r,\lambda,z,w,A}$ be the measure on self-avoiding excursions in $A\subsetneq\mathbb{Z}^2$ from $z$ to $w$, assigning an excursion $\omega$ mass … where $m^*(A;\omega)$ is t…

Uniqueness conjecture. For every $0<\theta\leq1$, the LCC assignment whose existence is asserted in Theorem 1 is unique up to multiplication by a scalar factor.

Limiting measure conjecture. For $r=1$, the limiting measure

Canonical extremal measure conjecture. For every $r\in(0,1)$, the measure {\text{\boldmath{pi}}}^{(r)} on the pullback image of $\Upsilon^{-1}(r)$ is induced by

Let $H$ be the height function on universal Teichmüller space, let $u0$ be the associated measure, and let $beta0=2pi^2cdot(1/8)$, where $1/8$ is a critical exponent from logarith…

Let $\operatorname{c}$ be a parameter with $\operatorname{c}\le 1$. Consider simple loops in a Riemann surface and measures on them taking values in a certain determinant bundle. K…

A configuration is either a pair $(\ell,\Sigma)$ consisting of a Riemann surface $\Sigma$ and a loop $\ell\subset\Sigma$, or a triple $(\ell,\Sigma_1,\Sigma_2)$ consisting of Riema…

Let $\mu_0$ be Werner's measure, let $\mu_c$ be the conjectural family deforming $\mu_0$, and let $\mathcal W\times\overline{\mathcal W}$ denote the conformal vector fields acting…

For each Riemann surface $S$, let $\operatorname{Loop}(S)$ be the space of loops in $S$, let $\operatorname{Det}\to\operatorname{Loop}(S)$ be the continuous positive determinant li…