Related papers: Topology in Physics - A Perspective

We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries-long studies. We discuss their multifunctional role in modern physics…

This article is a very short introduction to pcf theory for topologists.

The Hopfield model, originally inspired by spin-glass physics, occupies a central place at the intersection of statistical mechanics, neural networks, and modern artificial intelligence. Despite its conceptual simplicity and broad…

We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.

Ren{\'e} Thom discovered several refined topological notions in the writings of Aristotle, especially the biological. More generally, he considered that some of the assertions of the Greek philosophers have a definite topological content,…

Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…

In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.

Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…

Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…

Nuclear Physics is the branch of physics that deals with the properties and structure of matter on the hadronic level. In this article we review briefly the history of this field, which has a major role in the development of our…

We survey some results on toric topology.

A large class of physical systems involves the vanishing of a 1-form on a manifold as a constraint on the acceptable states. This means that one is always dealing with the Pfaff problem in those cases. In particular, knowing the degree of…

Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…

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

We discuss how developments in physics often imply in the need that spacetime acquires an increasingly richer and complex structure. General Relativity was the first theory to show us the way to connect space and time with the physical…

In the period from about 1890 to 1915 an interdisciplinary and unifying research programme known as "cosmical physics" attracted much scientific and public attention. It typically included aspects of the earth sciences (such as magnetic…

Different types of Lifshitz transitions are governed by topology in momentum space. They involve the topological transitions with the change of topology of Fermi surfaces, Weyl and Dirac points, nodal ines, and also the transitions between…

Whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental long-standing questions in cosmology. These questions of topological nature have become particularly topical, given the wealth of…

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…

In these three lectures, I review the physics of top quark. Each of the lectures is self-contained.