Related papers: $\mathbb{F}_1$ for everyone
In this lecture I build up the motivation for relativity and gravitation based on general principles and common sense considerations which should fall in the sphere of appreciation of a general reader. There is a novel way of looking at…
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…
Lecture script of a one-semester course that aims to develop an understanding and appreciation of fundemental concepts in modern physics for students who are comfortable with calculus. This document contains the first six lessons that will…
Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…
Isaak Moiseevich Yaglom deduced complete classification of geometric spaces. In this work, supposed to your attention, author formalizes Yaglom's approach and constructs uniform theory of geometric spaces on analytic level. Among its…
This paper develops a theory of analytic geometry over the field with one element. The approach used is the analytic counter-part of the Toen-Vaquie theory of schemes over F_1, i.e. the base category relative to which we work out our theory…
These notes aim to give an introduction to a few aspects of noncommutative geometry.
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…
The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.
I give an overview of the motivations for and theory/phenomenology of supersymmetry.
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
The first free comprehensive textbook on quantum (and classical) field theory. The approach is pragmatic, rather than traditional or artistic: It includes practical techniques, such as the 1/N expansion (color ordering) and spacecone…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…
This is the written version of a lecture given at the ``VI Mexican School of Gravitation and Mathematical Physics" (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…