Related papers: The Maslov dequantization, idempotent and tropical…

We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…

An introduction in quantum mechanical theory for NMR students which covers basic concepts and calculations.

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

This work provides a thorough introduction to the field of gammoids and presents new results that are considered helpful for solving the problems of recognizing and coloring gammoids.

This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.

This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.

This paper briefly summarizes previous work on complex classical mechanics and its relation to quantum mechanics. It then introduces a previously unstudied area of research involving the complex particle trajectories associated with…

A brief introduction to the theory and phenomenology of soft interactions is given, focusing on total and elastic cross sections and multiparticle production.

In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…

We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of…

The aim of this lecture is to discuss in some detail two simple but important problems which have considerable importance for the development of theoretical work in semiclassical dense matter physics.

The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.

An expository hitchhikers guide to some theorems in mathematics.

This is an informal introduction to the ideas of decoherence and emergent classicality, including a simple account of the decoherent histories approach to quantum theory. It is aimed at undergraduates with a basic appreciation of quantum…

We present a brief introduction to the topological phases of matter. This is a brief review article written for the Boletin de la Sociedad Mexicana de Fisica

An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.

This is an expository paper (in Spanish) about the metric approximation of groups.

We review the features of Dark Matter as a particle, presenting some old and new instructive models, and looking for their physical implications in the early universe and in the process of structure formation. We also present a schematic of…

We give a formula for matrix exponentials and partial fraction decompositions.

We introduce the notion of induced Maslov cycle, which describes and unifies geometrical and topological invariants of many apparently unrelated problems, from Real Algebraic Geometry to sub-Riemannian Geometry.