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Geometry and Physics: Volume I – A Festschrift in honour of Nigel Hitchin - Oxford Scholarship Online
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Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Abstract

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic an ... More

Keywords: geometry, mathematical physics, algebraic geometry, moduli space, Higgs bundle

Bibliographic Information

Print publication date: 2018 Print ISBN-13: 9780198802013
Published to Oxford Scholarship Online: December 2018 DOI:10.1093/oso/9780198802013.001.0001

Authors

Affiliations are at time of print publication.

Andrew Dancer, editor
Professor of Mathematics, Mathematical Institute, Oxford University

Jørgen Ellegaard Andersen, editor
Professor of Mathematics, Aarhus University

Oscar García-Prada, editor
CSIC Research Professor, Consejo Superior de Investigaciones Cientificas (CSIC),

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Contents

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Front Matter

Title Pages

Preface

Part I Volume I

1 Boundary Value Problems for the Lorentzian Dirac Operator

Christian Bär, Sebastian Hannes, Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany, Email: baer@math.uni-potsdam.de, shannes@math.uni-potsdam.de

2 Torsion of Elliptic Curves and Unlikely Intersections

Fedor Bogomolov1,2 Hang Fu1 Yuri Tschinkel1,3 1 Courant Institute of Mathematical Sciences, N.Y.U. 251 Mercer Str., New York, NY 10012, U.S.A. Email: fu@cims.nyu.edu 2 National Research University Higher School of Economics, Russian Federation, AG Laboratory, HSE, 7 Vavilova Str., Moscow, Russia, 117312, Email: bogomolo@cims.nyu.edu 3 Simons Foundation, 160 Fifth Av., New York, NY 10010, U.S.A., Email: tschinkel@cims.nyu.edu

3 Algebras of Quantum Monodromy Data and Character Varieties

Leonid Chekhov1 Marta Mazzocco2 Vladimir Rubtsov3 1 Steklov Mathematical Institute of Russian Academy of Sciences and Laboratoire Poncelet, Moscow, Russia, and Michigan State University, East Lansing, USA. Email: chekhov@mi.ras.ru. 2 School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom. Email: m.mazzocco@bham.ac.uk. 3 Université d’Angers, France and Theory Division, ITEP; Moscow, Russia; Email: volodya@univ-angers.fr.

4 The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics

Tristan C. Collins, Dan Xie, Shing-Tung Yau, Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, MA 02138, USA Email: tcollins@math.harvard.edu, dxie@cmsa.fas.harvard.edu, yau@math.harvard.edu

5 Quaternionic Geometry in Dimension 8

Diego Conti, Thomas Bruun Madsen, Simon Salamon, Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 55, 20125 Milano, Italy. Email: diego.conti@unimib.it Department of Mathematics, Aarhus University, Ny Munkegade 118, Bldg 1530, 8000 Aarhus, Denmark. Email: thomas.madsen@math.au.dk Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK. Email: simon.salamon@kcl.ac.uk

6 Boundary Value Problems in Dimensions 7, 4 and 3 Related to Exceptional Holonomy

Simon Donaldson

7 A Hitchin Connection for a Large Class of Families of Kähler Structures

Jørgen Ellegaard Andersen, Kenneth Rasmussen, Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, University of Aarhus, DK-8000 Aarhus, Denmark. Email: andersen@imf.au.dk

8 The Taub–NUT Ambitoric Structure

Paul Gauduchon, Paul Gauduchon, CMLS, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France. Email: paul.gauduchon@polytechnique.edu.

9 Mirror Symmetry with Branes by Equivariant Verlinde Formulas

Tamás Hausel1 Anton Mellit2 Du Pei3 1 IST Austria Email: tamas.hausel@ist.ac.at 2 University of Vienna Email: anton.mellit@univie.ac.at 3 QGM, Aarhus University Walter Burke Institute for Theoretical Physics, Caltech Email: pei@caltech.edu

10 Deformation Theory of Lie Bialgebra Properads

Sergei Merkulov1 Thomas Willwacher2 1 Sergei Merkulov: Mathematics Research Unit, Luxembourg University, Maison du Nombre, 6 Avenue de la Fonte, L-4364 Esch-sur-Alzette, Grand Duchy of Luxembourg, Email: sergei.merkulov@uni.lu 2 Thomas Willwacher: Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092 Zurich, Switzerland, Email: thomas.willwacher@math.ethz.ch

11 Vertex Algebras and 4-Manifold Invariants

Mykola Dedushenko1,3 Sergei Gukov1,3 Pavel Putrov2 1 Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA 2 School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA 3 Centre for Quantum Geometry of Moduli Space, Department of Mathematics, Aarhus University Aarhus, DK-8000, Denmark

12 Hyperfunctions, the Duistermaat–Heckman Theorem and Loop Groups

Lisa C. Jeffrey, James A. Mracek, Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George Street, Room 6290, Toronto, ON, Canada M5S2E4 Email: jmracek@math.toronto.edu, jeffrey@math.toronto.edu

13 Quantization of the Quantum Hitchin System and the Real Geometric Langlands Correspondence

Jörg Teschner, Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany, and: DESY theory, Notkestrasse 85, 20607 Hamburg, Germany