相关论文: Lectures on Integrability of Lie Brackets

Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).

Lecture notes reviewing most recent developments in string/M/brane theory given by C. G. at the CIME Summer International Center of Mathematics at Cetraro. July 1997.

These are notes for a summer course given at the PIMS Summer School on Geometric and Topological Aspects of the Representation Theory of Finite Groups in Vancouver, July 27-30 2016.

These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…

We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the…

An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.

Integrable Hamiltonian systems on symplectic manifolds have been well-studied. However, an intrinsic property of these kind of systems is that they can only live on even dimensional manifolds. To introduce a similar notion of integrability…

This paper investigates different Poisson structures that have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. Our aim is to explore the main brackets which have been proposed and to…

These are notes from a 3-lecture course given by V. Dokchitser at the ICTP in Trieste, Italy, 1st--5th of September 2014, as part of a graduate summer school on "L-functions and modular forms". The course is meant to serve as an…

In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a…

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

Lectures presented at the Spring School, Trieste, Italy 1993.

Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.

Lectures given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009

We review an approach to the construction and classification of p-brane solitons in arbitrary dimensions, with an emphasis on those that arise in toroidally-compactified M-theory. Procedures for constructing the low-energy supergravity…

These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on…

These lectures notes were written for a summer school on Mathematics for post-quantum cryptography in Thi\`es, Senegal. They try to provide a guide for Masters' students to get through the vast literature on elliptic curves, without getting…

An extended summary of the lecture course given at the V School on Geometry and Physics, Bia\l owe\.za 2016, in which an algebraic approach to differentiation and integration that is characteristic for non-commutative geometry is described.

These notes are an account of a series of lectures given at the Les Houches Summer School "Active Matter and Non-equilibrium Statistical Physics" during August and September 2018.