Related papers: Adventures in algebraic geometry
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
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.
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
Notes prepared for the introductory general relativity course PHYSICS 748 at The University of Auckland. They are designed to introduce general relativity to upper-year undergraduate students directly using the modern language of…
We develop the idea of using an algebraic-geometry approach to classical differential geometry problems. Consider an orthogonal net constructed according to algebraic-geometric data we obtain a set of smooth orthogonal nets that are…
This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…
This is a slightly revised version of lectures notes for a course in Summer 2022 joint between Bonn and Copenhagen, intended as a stable citable version. The goal of this course is to make our general approach to analytic geometry via…
These notes give an introduction to the Gabriel-Roiter measure of a finite dimensional algebra. They are based on a series of four lectures at the "Advanced School and Conference on Representation Theory and Related Topics" in Trieste…
This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
The note complements topological aspects of the theory of chiral algebras.
While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…