Related papers: A short course on Tensor algebra and analysis, wit…
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required…
This text is the support for the course of Modeling of Solids, of the Master of Mechanics of the University Paris-Saclay - Curriculum MMM: Mathematical Methods for Mechanics, held at Versailles. The course is the continuation of the course…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
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.
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…
The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Algebraic basics on Temperley-Lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.
We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their…
These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so called parabolic geometries.
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in…
In this expository paper we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical…
The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…