Related papers: Dualities and Twins: Reflections on Hapgood
Withdrawn; note hep-th/0110236 covers some similar material.
This is the written version of the supersymmetry lectures delivered at the 30th and 31st British Universities Summer Schools in Theoretical Elementary Particle Physics (BUSSTEPP) held in Oxford in September 2000 and in Manchester in…
A talk presented at International Conference ICMP-2000, London, England
We present a review of heterotic-type I string duality. In particular, we discuss the effective field theory of six- and four-dimensional compactifications with N>1 supersymmetries. We then describe various duality tests by comparing gauge…
This is the written version of the opening talk at the symposium "Expectations of a Final Theory," at Trinity College, Cambridge, on September 2, 2005. It is to be published in Universe or Multiverse?, ed. B. Carr (Cambridge University…
These lecture notes form an expanded account of a course given at the Summer School on Topology and Field Theories held at the Center for Mathematics at the University of Notre Dame, Indiana during the Summer of 2012. A similar lecture…
Notes of my 14 `lectures on everything' given at the 1995 Les Houches school. An introductory course in topological and conformal field theory, strings, gauge fields, supersymmetry and more. The presentation is more mathematical then usual…
Lecture notes delivered in Barcellona in the fall of 2003
Lecture notes for the tutorial at the workshop HPOPT 2008 - 10th International Workshop on High Performance Optimization Techniques (Algebraic Structure in Semidefinite Programming), June 11th to 13th, 2008, Tilburg University, The…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
Impact of academic research onto the non-academic world is of increasing importance as authorities seek return on public investment. Impact opens new opportunities for what are known as "professional services": as scientometrical tools…
These are expanded lecture notes for a minicourse taught at the "School on disordered media" at the Alfred Renyi institute in Budapest, January 2025.
This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi…
We give a survey on classical and recent results on dual spaces of topological tensor products as well as some examples where these are used.
Remarks on Michael Frayn's play "Copenhagen".
These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in…
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in…
This note is an extended version of my presentation at the "Focused Research Workshop on Exterior Di{\S}erential Systems and Lie Theory" held at the Fields Institute in Toronto, December 9-13, 2013. Some ideas and constructions of this note…
These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of…
These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.