Related papers: Geometry in the Transition from Primary to Post-Pr…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
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…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
The purpose of this book is to give an exposition of geometry, from a point of view which complements Klein's Erlangen program. The emphasis is on extending the classical Euclidean geometry to the finite case, but it goes beyond that. After…
Our aim is to give a friendly introduction for students to systolic inequalities. We will stress the relationships between the classical formulation for Riemannian metrics and more recent developments related to symplectic measurements and…
Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important…
This text is an introduction to algebraic enumerative geometry and to applications of tropical geometry to classical geometry, based on a course given during the X-UPS mathematical days, 2008 May 14th and 15th. The aim of this text is to be…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
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…
We show how Cartesian method can be used in the proof of fundamental planimetric topics of the school course, such as introduction of trigonometric functions, equation of a line and similarity of triangles. This work also can be considered…
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…
This paper focuses on a new approach to plane geometry and develops important concepts that can allow researchers to unite and observe plane geometry from a new, meaningful perspective.
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
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…
This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems through algebraic geometry and representation theory. This article gives a high-level exposition of the basic plan of GCT based on the principle,…