Related papers: Lectures notes in universal algebraic geometry
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
Lecture notes on Finsler Geometry
Some examples and basic properties of ultrametric spaces are briefly discussed.
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
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…
These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.
We discuss new problems in universal algebraic geometry and explain them by boolean equations.
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
These notes aim to give an introduction to a few aspects of noncommutative geometry.
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Lecture notes for an introductory course in elementary particles.
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…
These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
A short survey on applications of algebraic geometry in topological data analysis.
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…
Lecture notes on selected topics in the theory of gravitation.
These are the notes from my courses on the arithmetic of quadratic forms.