相关论文: Ueber die Geometrie der alten Aegypter

Summary talk at ICHEP 2002, Amsterdam, July 2002. I have kept very close to the content and style of the talk as it was delivered. You may access the associated PowerPoint presentation through a link at…

Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some theorems. These are slightly enhanced preparation notes for a talk given at the joint AMS meeting of January 16, 2014 in…

The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.

This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…

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,…

The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…

Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006. Typos corrected, some refernces added.

This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…

These are partial lecture notes from the fifteen Ess\'en Lectures for graduate students at Uppsala University given (in four days!) in June 2013.

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…

How were surfaces evaluated before the invention of the sexagesimal place value notation in Mesopotamia? This chapter examines a group of five tablets containing tables for surfaces of squares and rectangles dated to the Early Dynastic…

These are excerpts from the closing talk at the "XIIth Conference on Quark Confinement and the Hadron Spectrum", which took place last Summer in Thessaloniki --an excellent place to enjoy an interest in archeology. A more complete personal…

In this article, I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us (the…

We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.

The following notes are intended to make a small digression on the topics mentioned in the title of the same, since these were not addressed in the past tribute by the Institute of Physics of the UdeA. We believe more than platitude try to…

We discuss Einstein's knowledge of projective geometry. We show that two pages of Einstein's Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his…

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…

These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}). The lectures are meant to be accessible to advanced…