Related papers: Lectures on Integrability of Lie Brackets
This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.
Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras.…
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
This volume contains the proceedings of the Ninth Workshop on Fixed Points in Computer Science which took place on the September 1st, 2013 in Torino, Italy as a CSL-affiliated workshop. Past workshops have been held in Brno (1998, MFCS/CSL…
This is a brief review paper summarizing talks at the NATO school on Complexity and Large Deviations in Geilo, Norway, 2001.
These are the notes corresponding to the course given at the IAS-Park City graduate summer school in July 2007.
The BRIDGES meeting in gauge theory, extremal structures, and stability was held in June 2024 at l'Institut d'\'Etudes Scientifiques de Carg\`ese in Corsica, organized by Daniele Faenzi, Eveline Legendre, Eric Loubeau, and Henrique S\'a…
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
These are the lecture notes (in Italian) of a course held in Perugia, Italy, during the summer 2002. They concern the basic facts on the iterative solution of linear systems. The course is self-contained and requires only basic knowledge of…
Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
A local classification of all Poisson-Lie structures on an infinite-dimensional group $G_{\infty}$ of formal power series is given. All Lie bialgebra structures on the Lie algebra ${\Cal G}_{\infty}$ of $G_{\infty}$ are also classified.
These lecture notes review the structure of anomalies and present some of their applications in field theory, string theory and M theory. They expand on material presented at the TASI 2003 summer school and the 2005 International Spring…
We give an introduction to the structure theory of extended affine Lie algebras, which provide a common framework for finite-dimensional semisimple, affine and toroidal Lie algebras. The notes are based on a lecture series given during the…
This paper comprises the written version of the lectures on string theory delivered at the 31st British Universities Summer School on Theoretical Elementary Particle Physics which was held in Manchester, England, August 28 - September 12…
We survey the contributions presented in the working group "Diffraction & Vector Mesons" at the XIII International Workshop on Deep Inelastic Scattering (http://www.hep.wisc.edu/dis05)
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…
This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
These notes are a written version of a set of lectures given at TASI-02 on the topic of precision electroweak physics.