Related papers: Dualities and Twins: Reflections on Hapgood

``When to the sessions of sweet silent thought I summon up re-membranes of things past, I sigh the lack of many a thing I sought''. (Apologies to William Shakespeare)

A survey of general results on the singularities of inverses to meromorphic functions is given, with applications to holomorphic dynamics. This is a lecture delivered at the workshop "The role of complex analysis in complex dynamics" in…

Notes on algebraic stacks, prepared for an 11-lecture course at the NCTS, Taipei, during the fall of 2022.

This text is related to the tutorials I gave at the Banff International Research Station and within a "Doc-course" at Charles University Prague in the fall of 2014. It describes my current research and some of the most important open…

The second part of a set of notes based on lectures given at the IHES in 2015 on Feynman amplitudes and motivic periods.

Lectures given at the Isaac Newton Institute, NATO-ASI School on "Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July, 1997.

These notes were written for the Cours Peccot given at the Coll\`ege de France in 2007.

These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic…

This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…

This is the extended write-up of a series of lectures on the duality between the Sine-Gordon model and the Thirring model. Prepared for the London Theory Institute (LonTI) - Fall 2022: a PhD-level mini-course, with exercises and a guide to…

This article is based on a talk given at a one-day meeting in NUI, Maynooth on the Fourth of April, 2008, held to honour David Walsh and Richard Watson. It surveys joint work with the author.

This article is an introduction for a theme issue following a Scientific Discussion Meeting on \emph{The next generation of analogue gravity experiments} held at the Royal Society in December 2019. This theme issue comprises a collection of…

On the evening after Stephen Hawking's funeral in Cambridge on March 31, 2018 a dinner for attendees who had come from far away was hosted by Paul Shellard, the Director of the Centre for Theoretical Cosmology. I was asked me to speak for…

Notes of an introductory course given at the conference "Torsors: Theory and Applications" in Edinburgh, January 2011.

This is the written version of two lectures given at the Newton Institute Euroconference on Duality and Supersymmetric Theories, Cambridge, England, 7-18 Apr 1997. It deals with the nature of supergravity vacua and black holes and black…

These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…

We discover that many natural-language prompts can be replaced by corresponding prompts that are unintelligible to humans but that provably elicit similar behavior in language models. We call these prompts "evil twins" because they are…

This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each…

This is a set of lectures given at the 99' Cargese Summer School: Particle Physics : Ideas and Recent Developments. They contain a pedestrian exposition of recent theoretical progress in non-perturbative field theory and string theory based…

These are expository notes based on a talk given at the Superschool on derived categories and D-branes at University of Alberta in July of 2016. The goal of these notes is to give a motivated introduction to the Strominger-Yau-Zaslow (SYZ)…