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Full Description
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.
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, Madsen-Weiss and homological stability for mapping class groups of surfaces by N. Wahl Lectures on the Madsen-Weiss 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 Witten-Kontsevich 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
