Related papers: Non-Archimedean Geometry and Physics on Adelic Spa…
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
In this article, we will introduce methods of non-standard analysis into projective geometry. Especially, we will analyze the properties of a projective space over a non-Archimedean field. Non-Archimedean fields contain numbers that are…
Geometrical properties of holonomic and non holonomic varieties defined by the Pfaff equations connected with a first order systems of differential equations are studied. The Riemann extensions of affine connected spaces for investigation…
This paper is a very brief and gentle introduction to non-commutative geometry geared primarily towards physicists and geometers. It starts with a brief historical description of the motivation for non-commutative geometry and then goes on…
We study dynamical systems using measures taking values in a non-Archimedean field. The underlying space for such measure is a zero-dimensional topological space. In this paper we elaborate on the natural translation of several notions,…
A short survey on applications of algebraic geometry in topological data analysis.
We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.
We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle-Hawking proposal does not work in models with matter fields. p-Adic and adelic minisuperspace quantum cosmology…
This paper deals with various topics in analysis on hyperbolic spaces. It surveys some recent progress in non-Euclidean Fourier Analysis and proves some new results for the geodesic Radon transform on hyperbolic spaces.
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of…
Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured…
Gravity with incorporation of additional dimensions and noncommutative geometry.
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
Part 1 : For more than two millennia, ever since Euclid's geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time,…