Related papers: Model spaces: a survey
This is a short survey of amenable equivalence relations.
Tropical geometry is a relatively recent field in mathematics created as a simplified model for certain problems in algebraic geometry. We introduce the definition of abstract and planar tropical curves as well as their properties,…
The theme of this survey is that subgroups of the mapping class group of a finite type surface S can be studied via the geometric/dynamical properties of their action on the Thurston compactification of the Teichmuller space of S, just as…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…
Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary…
These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group…
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
Let $G/H$ be a semisimple symmetric space. Then the space $L^2(G/H)$ can be decomposed into a finite sum of series representations induced from parabolic subgroups of $G$. The most continuous part of the spectrum of $L^2(G/H)$ is the part…
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of…
This paper presents the authors' vision of the emerging field of spacetime metamaterials in a cohesive and pedagogical perspective. For this purpose, it systematically builds up the physics, modeling and applications of these media upon the…
In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
A few corrections and comments are made upon a previously published paper by the author (Gen. Rel. Gravit. 24, 199 (1992)), on the subject of cosmological models with compact spatial sections.
The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. Also, space limitation does not…