Related papers: Adic Spaces
We introduce type annotations as a flexible typing mechanism for graph systems and discuss their advantages with respect to classical typing based on graph morphisms. In this approach the type system is incorporated with the graph and…
Ad hoc abbreviations are commonly found in informal communication channels that favor shorter messages. We consider the task of reversing these abbreviations in context to recover normalized, expanded versions of abbreviated messages. The…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.
Double coset spaces of adelic points on linear algebraic groups arise in the study of global fields; e.g., concerning local-global principles and torsors. A different type of double coset space plays a role in the study of semi-global…
The goal of this note is to spell out the (apparently well-known and intuitively clear) notion of abelian category over an algebraic stack. In the future we will discuss the (much less evident) notion, when instead of an abelian category…
This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…
Lecture notes for an introductory course in elementary particles.
The OpenCitations organization is working on ingesting citation data and bibliographic metadata directly provided by the community (e.g., scholars and publishers). The aim is to improve the general coverage of open citations, which is still…
Citation indexes are by now part of the research infrastructure in use by most scientists: a necessary tool in order to cope with the increasing amounts of scientific literature being published. Commercial citation indexes are designed for…
Mathematical notations around the world are diverse. Not as much as requiring computing machines' makers to adapt to each culture, but as much as to disorient a person landing on a web-page with a text in mathematics. In order to understand…
This note provides a brief introduction to Redis highlighting its usefulness in multi-lingual statistical computing.
Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals…
This is a survey of results on the classification of Banach spaces as metric spaces. It is based on a series of lectures I gave at the Functional Analysis Seminar in 1984-1985, and it appeared in the 1984-1985 issue of the Longhorn Notes. I…
We show that the definition of an algebraic basis for a vector space allows the construction of an isomorphism with the one here called Algebraic Vector Space. Although the concept does not bring anything new, we mention some of the…
A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
These are lecture notes on string theory at Fudan University.