Related papers: Alexander Arhangel'skii
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
The purpose of this short paper dedicated to the 60th anniversary of Prof.Constantin Tsallis is to show how the use of mathematical tools and physical concepts introduced by Burr, L\.{e}vy and Tsallis open a new line of analysis of the old…
Notes on algebraic stacks, prepared for an 11-lecture course at the NCTS, Taipei, during the fall of 2022.
The recent opinion article "A decade of molecular cell atlases" by Stephen Quake narrates the incredible single-cell genomics technology advances that have taken place over the last decade, and how they have translated to increasingly…
This is a paper in Analytic Topology.
The process launched by Lobachevsky. The movement of the Kazan school of geometry towards physics. Personal memories of Alexei Zinovievich Petrov, the great Kazan geometer and theoretical physicist, who became the Author's Guiding Star.…
2023 year marks the hundredth birth anniversary of prominent Russian mathematician and thinker Igor Rostislavovich Shafarevich (1923-2017). The article presents a selection of quotations from various works of him, devoted to the future of…
We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to…
This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.
These are the extended notes of a talk I gave at the Geometric Topology Seminar of the Max Planck Institute for Mathematics in Bonn on January 30th, 2012. My goal was to familiarize the topologists with the basics of arithmetic hyperbolic…
The cover of the SIAM Journal on Applied Algebra and Geometry shows seven pictures. We describe these pictures and discuss the topics they represent. About the Author: Anna Seigal is a graduate student at UC Berkeley working in applied…
These brief remarks have been prepared in connection with a conference in honor of my thesis advisor, Richard Rochberg.
We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each branch. The skeleton of these notes was provided by the author's…
A report at Arbeitstagung, June 1999, Bonn, on the joint work with V.Gorbounov, F.Malikov and A.Vaintrob.
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
This article is a transcription of a video of a 1972 lecture by Jean Dieudonn\'e, enhanced with composite still images from the video. The lecture covers the same material as an earlier paper and lecture notes by Dieudonn\'e, but the live…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
This is the first part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi Huang in the conference on Monster and vertex operator algebras at the Research Institute…