Related papers: Lecture Notes on Quadratic Forms and their Arithme…
These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
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…
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 are notes from a basic course in Several Complex Variables
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
Brief lecture notes for a course about random matrices given at the University of Cambridge.
The note complements topological aspects of the theory of chiral algebras.
Lecture notes on selected topics in the theory of gravitation.
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
Lecture notes for an introductory course in elementary particles.
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
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.
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.
These are notes for a graduate-level introductory course on singularity categories.