Related papers: A glimpse into Thurston's work

Some geometric structures with associated Riemannian metrics have been considered in the book.

This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…

Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.

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…

This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…

In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…

Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…

In this note, we discuss the role played by the techniques from the "foundations of geometry" and in particular by Desargues' Theorem in the work of Busemann. This note is part of a forthcoming edition of Busemann's collected papers.

We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.

This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).

This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.

This paper provides a comprehensive overview of the current state of research on Douglas curvature in Finsler spaces. It explores the significance, properties, and applications of Douglas curvature, and its role in understanding Finsler…

We develop the theory of Thurston maps that are defined everywhere on the topological sphere $S^2$ with a possible exception of a single essential singularity. We establish an analog of the celebrated W. Thurston's characterization theorem…

This is a problem list in the theory of foliations and laminations of 3-manifolds. The focus is on the relationship of foliations and laminations with other aspects of 3-manifold topology, especially with the Thurston theory of geometric…

This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…

This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been…

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.

The author of this letter to the editor would like to set forth the argument that scientometrics is currently in a phase in which a taxonomic change, and hence a revolution, is taking place. One of the key terms in scientometrics is…

I review some of the scientific work of George Papadopoulos in the context of the Greek cultural tradition and modern theoretical physics. The main emphasis is on his works on path integrals and their applications. The review is closed by…

I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of…