相关论文: Mathematics, physics and philosophy in Riemann's w…

In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…

The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses…

An attempt is made of giving a self-contained (although incomplete) introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component…

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

These are lecture notes for the course "MATS4120 Geometry of geodesics" given at the University of Jyv\"askyl\"a in Spring 2020. Basic differential geometry or Riemannian geometry is useful background but is not strictly necessary. Exercise…

We present a set of lectures on topics of advanced calculus in one real and complex variable with several new results and proofs on the subject, specially with detailed proof-always missing in the literature - of the Cissoti explicitly…

Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…

Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure…

In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix…

This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…

I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be…

This is a survey of the work of Seiberg and Witten on 4-dimensional N=2 supersymmetric Yang-Mills theory and of some of its recent extensions, written for mathematicians. The point of view is that of algebraic geometry and integrable…

It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…

We present a brief review of Friedmann's impact on cosmology from a historical and a physical perspective.

We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy,…

We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and differential operations on forms, we obtain the structure…

This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between…

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity…