Moduli spaces of Riemann surfaces
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society ; [Princeton, New Jersey] : Institute for Advanced Study, [2013]
 Physical description
 x, 356 pages : illustrations ; 26 cm.
 Series
 IAS/Park City mathematics series ; v. 20.
Access
Available online

Stacks

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QA564 .M644 2013

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QA564 .M644 2013
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Contributors
 Contributor
 Farb, Benson, editor of compilation.
 Hain, Richard M. (Richard Martin), 1953 editor of compilation.
 Looijenga, E. (Eduard), 1948 editor of compilation.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 Introduction by B. Farb, R. Hain, and E. Looijenga A brief introduction to mapping class groups by Y. N. Minsky Teichmuller theory by U. Hamenstadt The Mumford conjecture, MadsenWeiss and homological stability for mapping class groups of surfaces by N. Wahl Lectures on the MadsenWeiss theorem by S. Galatius The Torelli group and congruence subgroups of the mapping class group by A. Putman Tautological algebras of moduli spaces of curves by C. Faber Mirzakhani's volume recursion and approach for the WittenKontsevich theorem on moduli tautological intersection numbers by S. A. Wolpert Teichmuller curves, mainly from the viewpoint of algebraic geometry by M. Moller Introduction to arithmetic mapping class groups by M. Matsumoto.
 (source: Nielsen Book Data)
 Publisher's Summary
 Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmuller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics.
(source: Nielsen Book Data)
Subjects
 Subject
 Moduli theory.
 Riemann surfaces.
 Algebraic geometry > Proceedings, conferences, collections, etc.
 Algebraic geometry > Curves > Families, moduli (algebraic)
 Several complex variables and analytic spaces > Deformations of analytic structures > Moduli of Riemann surfaces, Teichmüller theory.
 Algebraic topology > Fiber spaces and bundles > Homology of classifying spaces, characteristic classes.
 Manifolds and cell complexes > Topological transformation groups > Topological properties of groups of homeomorphisms or diffeomorphisms.
Bibliographic information
 Publication date
 2013
 Responsibility
 Benson Farb, Richard Hain, Eduard Looijenga, editors.
 Series
 IAS/Park City mathematics series ; volume 20
 ISBN
 9780821898871
 0821898876