相关论文: Lectures on Integrability of Lie Brackets

This article is a summary of four introductory lectures on ``Neutrino Experiments,'' given at the 2006 TASI summer school. The purposes were to sketch out the present questions in neutrino physics and to discuss the experimental challenges…

Lectures note for Cargese 99 Summer School Particle Physics: Ideas and Recent Development NATO Advanced Institute, Corsica, July 26-August 7, 1999

We study the geometric and algebraic properties of the twisted Poisson structures on Lie algebroids, leading to a definition of their modular class and to an explicit determination of a representative of the modular class, in particular in…

This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…

This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by…

These are the lecture notes from a course given in July 2005 at the summer school in Les Houches. We describe some recent results concerning two-dimensional conformally invariant systems. In particular, we discuss conformally invariant…

These are notes for a course on contact manifolds and torus actions delivered at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems at Centre de Recerca Matem\`atica in Barcelona in July 2001. To be published by…

This work concerns the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features: the Lie--Hamilton systems. We devise methods to study their superposition rules, time independent constants…

These lecture notes are based on a blackboard course given at the XVII Modave Summer School in Mathematical Physics held from 13 -- 17 September 2021 in Brussels (Belgium), and aimed at Ph.D. students in High Energy Theoretical Physics. We…

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…

We give explicit formulas for ten compatible Poisson brackets on $\mathbb P^5$ found in arXiv:2007.12351.

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

We present applications of tropical geometry to some integrable piecewise-linear maps, based on the lecture given by one of the authors (R. I.) at the workshop "Tropical Geometry and Integrable Systems" (University of Glasgow, July 2011),…

This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints. In particular, we clarify the geometric…

The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…

In this short survey, we describe our approach for constructing hierarchies of Poisson brackets for classical integrable systems using its' spectral curves.

A class of nongraded Hamiltonian Lie algebras was earlier introduced by Xu. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a ``sandwich'' method…

Lecture notes on selected topics in the theory of gravitation.

A review on topological strings and the geometry of the space of two dimensional theories. (Lectures given by C. Gomez at the Enrico Fermi Summer School, Varenna, July 1994)