Related papers: Integrable models with boundaries and defects

These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…

These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.

An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)

Four lectures given at Nankai Institute of Mathematics, Tianjin, China, 5--13 April 1991 present an elementary introduction into the quantum integrable models aimed for mathematical physicists and mathematicians. The stress is made on the…

This is an expanded and updated version of a lecture series I gave at Seoul National University in September 1997. It is in some sense an update of the 1979 Griffiths and Harris paper with a similar title. I discuss: Homogeneous varieties,…

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…

Lectures given at the Isaac Newton Institute, NATO-ASI School on "Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July, 1997.

These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge…

Invited talk delivered at the International Conference on General Relativity and Cosmology (ICGC), Ahmedabad, India; 13 - 18 December 1991. To appear in its proceedings.

These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

This text is based on a series of three expository lectures on a variety of topics related to "thin orbits," as delivered at Durham University's Easter School on "Dynamics and Analytic Number Theory" in April 2014. The first lecture reviews…

Talk presented at NATO Gran Finale Conference, Como, Italy, September 1993

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…

Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.

After reviewing some basic properties of RT algebras, which appear to be the natural framework to deal with integrable systems in presence of an impurity, we show how any integrable system (including these possessing translation invariance)…

Notes from a course given at Oujda university, Morocco, october 2002 - march 2003 within the support of a fellowship from the Agence Universitaire de la Francophonie. These notes present a brief introduction to Connes' non commutative…

These notes accompany an introductory lecture course on the twistor approach to supersymmetric gauge theories aimed at early-stage PhD students. It was held by the author at the University of Cambridge during the Michaelmas term in 2009.…

Lectures presented at the 42nd Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 1993.