Related papers: Lectures on Integrability of Lie Brackets

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.

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.…

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…

This is the text of the lecture given by the author in Naples at "Giornata IndAM", June 7, 2005. The lecture is addressed at the general mathematical audience and reviews several topics in deformation theory of associative algebras.

We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point of the general T-system and Y-system. We also study the…

The present text provides the lecture notes for the course "noise sensitivity and percolation" given at the 2010 Clay Summer School in Buzios, Brazil.

These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse…

These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.

This is a survey on the subject of the title corresponding to three lectures I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the Universita di Milano-Biccoca.

These are expanded lecture notes from the author's minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain. After giving a general introduction to wonderful varieties,…

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has…

Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory".

This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and…

These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.

Introduction to the Lecture Note Volume "ITEP Lectures in Particle Physics", including 25 years of personal reminiscences.

This paper is intended both an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past twenty years. It is…

Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.

This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.

This is a series of remedial lectures on open and unoriented strings for the heterotic string generation. The particular focus is on the interesting features that arise under T-duality---D-branes and orientifolds. The final lecture…