Related papers: Edinburgh Lectures on Geometry, Analysis and Physi…

These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.

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 an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…

This report is a combined version of two talks presented by the authors at the Edinburgh $b$-physics Workshop, December 1991. It presents the ideas of heavy quark symmetry and gives an introduction to some applications. The references…

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.

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.

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…

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 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.

These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…

These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…

The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…

These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…

This text is an introduction to a few selected areas of Alain Connes' noncommutative geometry written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It is an expanded version of my lectures which…

Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…

This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…

These are notes from my lecture at 4ECM in Stockholm (June 2004).

This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…