Related papers: Conformal Metrics
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
In the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.
This PhD thesis focuses on local conformal nets of von Neumann algebras on the circle. For a more detailed description of its content and of the results published within, see its preface.
We discuss a class of regions and conformal mappings which are useful in several problems of approximation theory, harmonic analysis and spectral theory.
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
A comprehensive introduction to two-dimensional conformal field theory is given.
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.
We discuss the recent results of the author on the existence of systems of differential equations for chiral genus-zero and genus-one correlation functions in conformal field theories.
This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are…