Related papers: Several Complex Variables

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…

These are the lecture notes for the introductory graduate course I taught at Yale during Spring 2007. I mostly followed [GS], [BGV], [AB], [Par2], and there are no original results in these notes.

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.

Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim…

These notes are a self-contained short proof of the stability of persistence diagrams.

These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…

In this note we give an algebraic and topological interpretation of essential coordinate components of characteristic varieties and illustrate their importance with an example.

Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…

The notes contain a streamlined account on stability of univariate polynomials and related problems

These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.

This note provides a tool to infer moderate deviations principles for specific random variables from deviations principles for their Hubbard-Stratonovich transforms.

This is a very basic introduction to some notions related to logic and complexity.

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

A stochastic dynamics framework for the study of complex systems is presented.

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

This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web…

These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.

These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.