In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was
designed to capture the mathematical essence of the Conformal Bootstrap formalism …

We demonstrate that the conformal loop ensemble (CLE) has a rich integrable structure by
establishing exact formulas for two CLE observables. The first describes the joint moments …

We demonstrate how to obtain integrability results for the Schramm‐Loewner evolution
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …

Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in
which the problem was reduced to the study of certain" random surfaces". He further made …

We prove that the probabilistic definition of the most general boundary three-point and bulk-
boundary structure constants in Liouville conformal field theory (LCFT) agree respectively …

Liouville conformal field theory (LCFT) is considered on a simply connected domain with
boundary, specializing to the case where the Liouville potential is integrated only over the …

Two-pointed quantum disks with a weight parameter W> 0 are a family of finite-area random
surfaces that arise naturally in Liouville quantum gravity. In this paper we show that …

We study (discretized)“random surfaces,” which are random functions from [special
characters omitted](or large subsets of [special characters omitted]) to either [special …

We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville
quantum gravity (LQG) in the supercritical (aka strongly coupled) phase, which corresponds …

In this document we prove higher equations of motion at the level $2 $ for boundary Liouville
Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyakov …