Related papers: Some remarks about homeomorphisms, "energy", and s…
Short survey to be published at the Encyclopedia of Mathematical Physics.
I review a number of the open questions about neutrino properties, critique recent hints of neutrino mass, and discuss one recently proposed neutrino mass matrix to illustrate the direction in which we may be headed. I also present one…
We study expansive dynamical systems from the viewpoint of general topology. We introduce the notions of orbit and refinement expansivity on topological spaces extending expansivity in the compact metric setting. Examples are given on…
Some basic sociophysical notions are described by a physicist, tentatively for a sociologically-oriented reader.
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.
In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum…
A brief overview of our current understanding of abundance and properties of dark energy and dark matter is presented. A more focused discussion of supersymmetric dark matter follows. Included is a frequentist approach to the supersymmetric…
We show that the differential-geometric description of matter by differential structures of spacetime leads to a unifying model of the three types of energy in the cosmos: matter, dark matter and dark energy. Using this model we are able to…
We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.
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
A brief review is offered of the theoretical background concerning dark energy: what is required by observations, what sort of models are being considered, and how they fit into particle physics and gravitation. Contribution to the SNAP…
This is an account of one man's view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
The paper reports on the solution in the semi-space corresponding to topological surface state. It was shown that the exponential surface state results from selection of the energy outside the allowed energy range. In the result, the…
We identify a class of linearly ordered topological spaces $X$ that may satisfy the property that $X\times X$ is homeomorphic to $X\times_l X$ or can be embedded into a linearly ordered space with the stated property. We justify the…
Typical properties of measure space automorphisms with respect to the Halmos and Alpern-Tikhonov metrics are discussed.
This is a survey on coarse geometry with an emphasis on coarse homology theories.
There has been, quite recently, a discussion on how holographic-inspired bounds might be used to encompass the present-day dark energy and early-universe inflation into a single paradigm. In the current treatment, we point out an…