Related papers: Adic Spaces
These notes introduce some of the basic mathematical and physical tools neccessary for theoretical investigations into the thermodynamics properties of light in cavities. The notes were created while preparing for a project in this area…
In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces…
These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.
This column advocates for including artificial intelligence (AI)-specific metadata on those academic papers that are written with the help of AI in an attempt to analyze the use of such tools for disseminating research.
The amount of data produced by large observational facilities and space missions has led to the archiving and on-line accessibility of much of this data, available to the entire astronomical community. This allows a much wider…
The Smithsonian/NASA ADS Abstract Service contains a wealth of data for astronomers and librarians alike, yet the vast majority of usage consists of rudimentary searches. Hints on how to obtain more focused search results by using more of…
These are notes on Zhang's work and subsequent developments produced in preparation for 5 hours of talks for a general mathematical audience given in Cambridge, Edinburgh and Auckland over the last year. Being for colloquium-style talks,…
This paper investigates mapping spaces between enriched operads and relates these spaces to those between operadic bimodules via convenient fiber sequences. The main statements hold for simplicial operads, operads enriched in simplicial…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
Some notes and observations on analytic functions defined on an annulus
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
These informal notes deal with some topics related to analysis on metric spaces.
Annotation graphs and annotation servers offer infrastructure to support the analysis of human language resources in the form of time-series data such as text, audio and video. This paper outlines areas of common need among empirical…
This brief exposition presents some basic properties of scalable monoids and quantity spaces, introduced in arXiv:1408.5024
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.
The digitisation campaigns carried out by libraries and archives in recent years have facilitated access to documents in their collections. However, exploring and exploiting these documents remain difficult tasks due to the sheer quantity…
This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…