Related papers: Edinburgh Lectures on Geometry, Analysis and Physi…
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
Three small lectures are devoted to three Newton's laws, lying in the foundation of classical mechanics. These laws are analyzed from the viewpoint of our contemporary knowledge about space, time and physical interactions. The lectures were…
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
Introduction to the Lecture Note Volume "ITEP Lectures in Particle Physics", including 25 years of personal reminiscences.
This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic…
These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.
Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.
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.
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
These expository notes are a somewhat embellished version of two rather informal evening review sessions given by the second author at the 2008 Bedlewo summer school on "Dynamical Systems - Geometric Structures and Rigidity"; they provide a…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
These are lecture notes for the course "MATS4120 Geometry of geodesics" given at the University of Jyv\"askyl\"a in Spring 2020. Basic differential geometry or Riemannian geometry is useful background but is not strictly necessary. Exercise…
Lecture notes of an algebraic geometry graduate course. The topics covered are as follows. Cohomology: ext sheaves and groups, cohomology with support, local cohomology, local duality. Duality: relative duality, Cohen-Macaulay schemes.…
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…
Physicists and physics students have been studied with respect to the variation in ways they expound on their topic of research and a physics problem, respectively. A phenomenographic approach has been employed; six fourth-year physics…
These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three lectures, we explain the main classical results (mainly due…
This article is a summary of four introductory lectures on ``Neutrino Experiments,'' given at the 2006 TASI summer school. The purposes were to sketch out the present questions in neutrino physics and to discuss the experimental challenges…
This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized. Lecture given at the ICCA7 conference, Toulouse (23/05/2005)
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…