Zobrazeno 1 - 10
of 226
pro vyhledávání: '"Guillarmou, Colin"'
This paper is the first part of the proof of the conformal bootstrap for Liouville conformal field theory on surfaces with a boundary, devoted to Segal's axioms in this context. We introduce the notion of Segal's amplitudes on surfaces with corners a
Externí odkaz:
http://arxiv.org/abs/2408.13133
For $R>0$, we give a rigorous probabilistic construction on the cylinder $\mathbb{R} \times (\mathbb{R}/(2\pi R\mathbb{Z}))$ of the (massless) Sinh-Gordon model. In particular we define the $n$-point correlation functions of the model and show that t
Externí odkaz:
http://arxiv.org/abs/2405.04076
In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the probabilistic constr
Externí odkaz:
http://arxiv.org/abs/2403.12780
In conformal field theory, the semigroup of annuli with boundary parametrization plays a special role, in that it generates the whole algebra of local conformal symmetries, the so-called Virasoro algebra. The subgroup of elements $\mathbb{A}_f=\mathb
Externí odkaz:
http://arxiv.org/abs/2403.10914
On a given Riemann surface, we construct a path integral based on the Liouville action functional with imaginary parameters. The construction relies on the compactified Gaussian Free Field (GFF), which we perturb with a curvature term and an exponent
Externí odkaz:
http://arxiv.org/abs/2310.18226
Let $\Sigma$ be a smooth closed oriented surface of genus $\geq 2$. We prove that two metrics on $\Sigma$ with the same marked length spectrum and Anosov geodesic flow are isometric via an isometry isotopic to the identity. The proof combines microlo
Externí odkaz:
http://arxiv.org/abs/2303.12007
Publikováno v:
Prob. Math. Phys. 5 (2024) 269-320
In this work, we construct a representation of the Virasoro algebra in the canonical Hilbert space associated to Liouville conformal field theory. The study of the Virasoro operators is performed through the introduction of a new family of Markovian
Externí odkaz:
http://arxiv.org/abs/2204.02745
The lens data of a Riemannian manifold with boundary is the collection of lengths of geodesics with endpoints on the boundary together with their incoming and outgoing vectors. We show that negatively-curved Riemannian manifolds with strictly convex
Externí odkaz:
http://arxiv.org/abs/2204.02476
Publikováno v:
Cambridge Journal of Mathematics, Vol. 12, No. 1 (2024), pp.165-222
For analytic negatively curved Riemannian manifold with analytic strictly convex boundary, we show that the scattering map for the geodesic flow determines the manifold up to isometry. In particular one recovers both the topology and the metric. More
Externí odkaz:
http://arxiv.org/abs/2201.02100
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 pioneered in physics by Belavin-Polyakov-Zamolodchikov. In Segal's formulatio
Externí odkaz:
http://arxiv.org/abs/2112.14859