Related papers: Sacler lectures
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free…
This is a lecture given July 14, 1993, at Nottingham.
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three lectures, we explain the main classical results (mainly due…
These lectures comprise the second half of a quantum field theory course given in 2004. Topics include the path integral, loop expansion, Feynman rules, various regularization methods, renormalization, running couplings and the…
This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the…
We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…
Lectures given at the Isaac Newton Institute, NATO-ASI School on "Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July, 1997.
Summary of three talks on the Holographic Space Time models of early universe cosmology, particle physics, and the asymptotically de Sitter final state of our universe.
Quantum groups have been studied within several areas of mathematics and mathematical physics. This has led to different approaches, each of them with their own techniques and conventions. Starting with Hopf algebras, where there is a…
Classical and quantum Chern-Simons with gauge group $\text{U}(1)^N$ were classified by Belov and Moore in \cite{belov_moore}. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a…
Complex vector fields with Maxwell, Chern-Simons and Proca terms are minimally coupled to an Abelian gauge field. The consistency of the spectrum is analysed and 1-loop quantum corrections to the self-energy are explicitly computed and…
These notes arose from three lectures on fusion system I gave at the University of Valencia in February 2023. We first consider fusion phenomena in classical group theory. Then we develop the abstract theory of fusion systems. Finally…
An encyclopedia article on mathematical aspects of quantum field theory in curved spacetime. Section titles are: Introduction and preliminaries; Construction of *-algebra for a real linear scalar field on globally hyperbolic spacetimes and…
Talk given at XIXth International Symposium on Lepton and Photon Interactions at High Energies (LP 99), Stanford, California, 9-14 August 1999.
The main concepts of the theory of tensors are presented. The emphasis is on the basic notions of tensor algebra and practical skills in culculations involving the Kronecker delta and Levi-Civita symbol. Sixty routine exercises are…
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
Talk given at NATO ARW in Kiev (September 2000) "Non-commutative Structures in Mathematics and Physics".