Related papers: Notes on splitting fields

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…

These are the notes from my courses on the arithmetic of quadratic forms.

For $m\geq 2$, we study derivations on symbol algebras of degree $m$ over fields with characteristic not dividing $m$. A differential central simple algebra over a field $k$ is split by a finitely generated extension of $k$. For certain…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.

This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.

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 notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.

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 provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.

We give a presentation of abelian class field theory.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

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…

A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…

These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…

In this paper we determine sufficient conditions for a quaternion algebra to split over a quadratic field. In the last section of the paper, we find a class of division symbol algebras of degree $n$ (where $n$ is a positive integer, $n\geq…

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.