Geometry and Physics: Two-Volume Pack A Festschrift in honour of Nigel Hitchin

by Ellegaard Andersen, Jørgen; Dancer, Andrew; García-Prada, Oscar

• ISBN13: 9780198802006
• ISBN10: 0198802005
• Format: Hardcover
• Copyright: 2018-12-25
• Publisher: Oxford University Press

Summary

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics.

These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

Author Biography

Jørgen Ellegaard Andersen obtained a DPhil in Mathematics from University of Oxford in 1992 and held assistant professor positions at University of California Berkeley and Aarhus University as well as general memberships at MSRI before obtaining a tenured position at Aarhus University in 1997. After being Clay Professor at University of California Berkeley, he became Professor of Mathematics at Aarhus University and he currently holds a Distinguished Visiting Professorship at California Institute of Technology. He is also Director of the Danish National Research Foundation Center of Excellence, Center for Quantum Geometry of Moduli Spaces (QGM) at Aarhus University.

Andrew Dancer took the degrees of BA and DPhil at Oxford University, and held postdoctoral fellowships at Cambridge, the Max-Planck-Institut, and IHES, before becoming a faculty member at McMaster University in Canada. He is now Professor of Mathematics at Oxford University and a Fellow of Jesus College.

Oscar García-Prada is a CSIC Research Professor at Instituto de Ciencias Matemáticas ICMAT, Madrid. He obtained a D.Phil. in Mathematics at the University of Oxford in 1991, and had postdoctoral appointments at Institut des Hautes Études Scientific (Paris), University of California at Berkeley, and University of Paris-Sud, before holding positions at University Autónoma of Madrid and École Polytéchnique (Paris). In 2002 he joined the Spanish National Research Council (CSIC).

Table of Contents

1. Boundary value problems for the Lorentzian Dirac operator, Christian Bar (Potsdam University), Sebastian Hannes (Potsdam University)
2. Torsion of elliptic curves and unlikely intersections, Fedor Bogomolov (Courant Institute of Mathematical Sciences, NYU), Hang Fu (Courant Institute of Mathematical Sciences, NYU), Yuri Tschinkel (Courant Institute of Mathematical Sciences, NYU)
3. Algebras of quantum monodromy data and character varieties, Leonid Chekhov (Steklov Mathematical Institute of Russian Academy of Sciences and Laboratoire Poncelet), Marta Mazzocco (Loughborough University), Vladimir Rubtsov (University of Angers and ITEP, Moscow)
4. The deformed Hermitian Yang-Mills equation in geometry and physics, Tristan Collins (Harvard University), Dan Xie (Harvard University), Shing-Tung Yau (Harvard University)
5. Quaternionic geometry in dimension 8, Diego Conti (Universita di Milano), Thomas Bruun Madsen (Aarhus University), Simon Salamon (King's College London)
6. Boundary value problems in dimensions seven, four and three related to exceptional holonomy., Simon Donaldson (Imperial and Simons Center, Stony Brook)
7. A Hitchin connection for a large class of families of Kahler structures, Jorgen Ellegaard Andersen (Aarhus University), Kenneth Rasmussen (Aarhus University)
8. The Taub-NUT ambitoric structure, Paul Gauduchon (Ecole Polytechnique)
9. Mirror symmetry with branes by equivariant Verlinde formulae, Tamas Hausel (Institute of Science and Technology Austria), Anton Mellit (Institute of Science and Technology Austria), Du Pei (Aarhus University and Caltech)
10. Deformation theory of Lie bialgebra properads, Sergei Merkulov (University of Luxembourg), Thomas Willwacher (ETH Zurich)
11. Vertex algebras and 4-manifold invariants, Mykola Dedushenko (Caltech), Sergei Gukov (Caltech), Pavel Putrov (Institute for Advanced Study, Princeton)
12. Hyperfunctions, the Duistermaat-Heckman theorem and loop groups, Lisa Jeffrey (University of Toronto), James Mracek (University of Toronto)
13. Quantisation of the quantum Hitchin system and the real geometric Langlands correspondence, Jorg Teschner (University of Hamburg)
14. Brauer group of moduli of Higgs bundles and connections, David Baraglia (University of Adelaide), Indranil Biswas (Tata Institute of Fundamental Research), Laura Schaposnik (University Illinois at Chicago)
15. Classification of boundary Lefschetz fibrations., Stefan Behrens (Utrecht University), Gil Cavalcanti (Utrecht University), Ralph Klaasse (Utrecht University)
16. SL(IF , R), Higgs bundles, and quantization, Olivier Biquard (École Normale Supérieure)
17. Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams, Philip Boalch (Universite Paris-Sud)
18. Irreducibility of moduli of semistable chains and applications to U(p,q)-bundles, Steven Bradlow (University of Illinois Urbana-Champaign), Oscar Garcia-Prada (Institute https://www.icmat.es/ of Mathematical Sciences), Peter Gothen (University of Porto), Jochen Heinloth (University of Duisburg)
19. Various generalisations and deformations of PSL(2,R) surface group representations and their Higgs bundles, Brian Collier (University of Maryland)
20. Restrictions of heterotic G_2 structures and instanton connections, Xenia de la Ossa (University of Oxford), Magdalena Larfors (Uppsala University), Eirek Svanes (Sorbonne University, Lagrange Institute)
21. Mixing Flows on Moduli Spaces of Flat Bundles over Surfaces, Giovanni Forni and William Goldman (University of Maryland)
22. Involutions of rank 2 Higgs bundle moduli spaces, Oscar Garcia-Prada (Institute https://www.icmat.es/ of Mathematical Sciences, Spain), Sundararaman Ramanan (Chennai Mathematical Institute)
23. Generalised Kahler metrics from Hamiltonian deformations, Marco Gualtieri (University of Toronto)
24. Stable Betti numbers of (partial) toroidal compactifications of the moduli space of Abelian varieties, Samuel Grushevsky (Mathematics Department, Stony Brook University), Klaus Hulek (, Leibniz University at Hannover), Orsola Tommasi (Chalmers University of Technology and the University of Gothenburg), Mathieu Dutour Sikiric (Rudjer Boskovi? Institute)
25. Spectral curves for the triple reduced product of coadjoint orbits for SU(3), Jacques Hurtubise (, McGill University), Lisa Jeffrey (University of Toronto), Steven Rayan (University of Saskatchewan), Paul Selick (University of Toronto), Jonathan Weitsman (Northeastern University)
26. Threefold extremal contractions of type (II A); part II, Shigefumi Mori (Research Institute for Mathematical Sciences, Kyoto University), Yuri Prokhorov (Steklov Mathematical Institute of Russian Academy of Sciences)
27. Parabolic Higgs bundles for real reductive Lie groups: a very basic introduction, Ignasi Mundet i Riera (Faculty of Mathematics and Computing, University of Barcelona)
28. Holonomic Poisson manifolds and deformations of elliptic algebras, Brent Pym (University of Edinburgh), Travis Schedler (Imperial College London)
29. An explicit view of the Hitchin fibration on the Betti side for P1 minus 5 points, Carlos Simpson (Universite Cote d'Azur, CNRS)