Related papers: Les Houches lecture notes on topological recursion
Physicists in search of the foundation of the world: how tiny objects can create matter, energy and even space and time - and possibly countless other universes. -- This article is meant as an introduction into quantum geometry (loop…
These are lecture notes of lectures presented at the 1993 Trieste Summer School, dealing with two classes of two-dimensional field theories, (topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these lectures is to…
On 13-01-2024 the annual wintersymposium of the Koninlijk Wiskundig Genootschap (KWG) was held in the academiegebouw in Utrecht. The symposium had the theme ``inzichtelijk abstract''. Thomas Rot gave a lecture on his favourite theorem from…
These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of…
I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…
These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics,…
I present a brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory. It is emphasized how the application of…
A set of four introductory lectures on Resurgent Asymptotics for Physics (``resurgence") at the CERN Summer School: Continuum Foundations of Lattice Gauge Theories, July 2024. Lecture 1: The Airy function and the Stokes phenomenon. Lecture…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for…
Some approaches to $2d$ gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different…
There has been recently considerable progress in understanding the nature of perturbation theory in UV free and gapped $2d$ integrable field theories with renormalon singularities. Thanks to Bethe ansatz and large $N$ techniques,…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
In a recent work [1] we consider the topological expansion for the non-mixed observables (including the free energy) for the formal Cauchy matrix model. The only restriction in [1] was the fact that all the branch points have to be simple.…
Lectures given at the Trieste Summer School, 1992. These notes are an update of my review article "Classical and Quantum W-Gravity", preprint QMW-92-1, published in in "Strings and Symmetries 1991", with some extra material on W-geometry,…
String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and…
A hallmark of the computational campaign in nuclear and particle physics is the lattice-gauge-theory program. It continues to enable theoretical predictions for a range of phenomena in nature from the underlying Standard Model. The…
The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their…
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…