相关论文: Topology and physics-a historical essay

We show that the number of gods in a universe must equal the Euler characteristics of its underlying manifold. By incorporating the classical cosmological argument for creation, this result builds a bridge between theology and physics and…

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.

We consider several appearances of the notion of convexity in Greek antiquity, more specifically in mathematics and optics, in the writings of Aristotle, and in art. The final version of this article will appear in the book `Geometry in…

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…

Modern cosmology poses deep and unavoidable questions for fundamental physics. In this plenary talk, delivered in slightly different forms at the {\it Particles and Nuclei International Conference} (PANIC05) in Santa Fe, in October 2005,…

Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…

While purely philosophical in the early times, and still very speculative at the beginning of the twentieth century, Cosmology has gradually entered into the realm of experimental science over the past eighty years. It has raised some…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

In a recent article we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models are treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential etc.). This model has the…

By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…

This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [arXiv:1002.0256] and [arXiv:1108.3370], while this survey focuses on…

This paper traces the seminal roles that physicists and mathematicians have played in the conceptual development of the biological sciences in the past, and especially in the 19th and 20th centuries.

This paper gives a short review of the history of statistical physics starting from D. Bernoulli's kinetic theory of gases in the 18th century until the recent new developments in nonequilibrium kinetic theory in the last decades of this…

The state of our understanding of cosmology is reviewed from an astrophysical cosmologist point of view with a particular emphasis given to recent observations and their impact. Discussion is then presented on the implications for particle…

Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…

Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…

The gedanken-experiment of Einstein's lift is analyzed in order of determining whether the free-falling observer inside the lift can detect the eventual topological non-triviality of space-time

This article is a brief survey of the theory of topological modular forms (TMF) and the theory of topological automorphic forms (TAF). It will be a chapter in forthcoming "Handbook of Homotopy Theory" edited by Haynes Miller.