Related papers: A brief introduction to Poisson geometry

We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher''…

These notes give an informal and leisurely introduction to $\mathrm{G}_2$ geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in $7$ dimensions that is the pointwise model for…

Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…

While the construction of symplectic integrators for Hamiltonian dynamics is well understood, an analogous general theory for Poisson integrators is still lacking. The main challenge lies in overcoming the singular and non-linear geometric…

This paper contains the material discussed in the series of three lectures that I gave during the workshop of the ICRA 2018 in Prague. I will introduce the reader to some of the techniques used in the study of the geometry of quiver…

The nine two-dimensional Cayley-Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogeneous spaces (of points and two kinds of lines), in such a…

We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and…

Tempered distributions on Rn that have the Poisson structure are characterized in terms of geometry of its support and spectrum

These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…

This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…

We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given…

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…

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure…

We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is intimately related to the group of…

A new approach to Poisson approximation is proposed. The basic idea is very simple and based on properties of the Charlier polynomials and the Parseval identity. Such an approach quickly leads to new effective bounds for several Poisson…

These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…

This is an expanded version of a three-hour minicourse given at the winterschool Winterbraids IV held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We…

Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed…

These notes aim to give an introduction to a few aspects of noncommutative geometry.

This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…