Related papers: A survey of J-spaces
This is the written version of a set of introductory lectures on string theory.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
This note describes how to construct toroidal polyhedra which are homotopic to a given type of knot and which admit an isohedral tiling of 3-space.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
The purpose of this paper is to formulate a number of conjectures giving a rather complete description of the tautological ring of M_g and to discuss the evidence for these conjectures.
In this note, we investigate estimates of the Morse index for F-harmonic maps into spheres, our results extend partially those obtained in ([14]) and ([15]) for harmonic and p-harmonic maps.
The aim of this paper is to study the vector valued de Branges spaces, which are based on $J$-contractive operator valued analytic functions, and to explore their role in the functional models for simple, closed, densely defined, symmetric…
This is a survey written for a special edition of the journal of differential geometry.
We give an informal, expository account of a project to construct completions of period maps.
In this paper, we introduce round and sleek topological spaces and study their properties.
This note is dedicated to the study of a Hopf module structures on the space of framed chord diagrams and framed graphs. We also introduce a framed version of the chromatic polynomial and propose two methods to construct framed weight…
The study of strings is an important combinatorial field that precedes the digital computer. Strings can be very long, trillions of letters, so it is important to find compact representations. Here we first survey various forms of one…
This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
The purpose of this note is to provide a short invitation to the universal algebraic approach to topological string theory. In the first section we make an attempt to explain the origin of this approach and how it fits into the bigger…
We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.
This is a continuation of the papers [Kuryakov-Sukochev, JFA, 2015] and [Sadovskaya-Sukochev, PAMS, 2018], in which the isomorphic classification of $L_{p,q}$, for $1< p<\infty$, $1\le q<\infty$, $p\ne q $, on resonant measure spaces, has…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
Let $X_{\bullet}$ denote a simplicial space. The purpose of this note is to record a decomposition of the suspension of the individual spaces $X_n$ occurring in $X_{\bullet}$ in case the spaces $X_n$ satisfy certain mild topological…