Related papers: Model Theory, Arithmetic & Algebraic Geometry
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts [64-66] that reflect a certain range of developments, but even in their totality they cannot be taken as a…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools…
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…
This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometry.
We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
Motivic homotopy theory is meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. As proved by Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to Voevodsky's…
The theory of matroids or combinatorial geometries originated in linear algebra and graph theory, and has deep connections with many other areas, including field theory, matching theory, submodular optimization, Lie combinatorics, and total…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
This is a first graduate course in algebraic geometry. It aims to give the student a lift up into the subject at the research level, with lots of interesting topics taken from the classification of surfaces, and a human-oriented discussion…
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…
To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…
``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts of an international community in many variants and with the…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…