Related papers: Volumes and Random Matrices
In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…
Weil-Petersson volumes are the volumes of the moduli spaces of bordered Riemann surfaces and have played an important role in the relationship between two-dimensional quantum gravity and algebraic geometry. In the last couple years progress…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
Based on the discovery of the duality between Jackiw-Teitelboim quantum gravity and a double-scaled matrix ensemble by Saad, Shenker and Stanford in 2019, we show how consistency between the two theories in the universal Random Matrix…
Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of these volumes has inspired remarkable…
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to prove via algebraic geometry a recursion between the…
These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
We review recent work in the lattice approach to random surfaces and quantum gravity. Our task is made somewhat easier by some very interesting results, particularly in four dimensions, that have appeared recently and which are reported…
This paper is mostly a survey of recent work on sequences of locally symmetric spaces whose Riemannian volume goes to infinity. We also work out some applications to random surfaces.
We show certain correlators in generic one-matrix models define a notion of ``discrete'' volumes of the moduli space of Riemann surfaces, generalizing the connection between random matrices and JT gravity. We prove they obey a discrete,…
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper…
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The…
This note aims to provide an entr\'ee to two developments in two-dimensional topological gravity -- that is, intersection theory on the moduli space of Riemann surfaces -- that have not yet become well-known among physicists. A little over…
We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by…
Volume of moduli space of BPS vortices on a compact genus h Riemann surface Sigma_h is evaluated by means of topological field theory and localization technique. Vortex in Abelian gauge theory with a single charged scalar field (ANO vortex)…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…