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OverviewThis book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program ``Geometry of moduli spaces and representation theory'', and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan-Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions. Full Product DetailsAuthor: Roman Bezrukavnikov , Alexander Braverman , Zhiwei YunPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.915kg ISBN: 9781470435745ISBN 10: 1470435748 Pages: 436 Publication Date: 30 December 2017 Audience: Professional and scholarly , College/higher education , Professional & Vocational , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsM. A. de Cataldo, Perverse sheaves and the topology of algebraic varieties X. Zhu, An introduction to affine Grassmannians and the geometric Satake equivalaence Z. Yun, Lectures on Springer theories and orbital intgegrals N. G. Chau, Perverse sheaves and fundamental lemmas A. Okounkov, Lectures on $K$-theoretic computations in enumerative geometry H. Nakajima, Lectures on perverse sheaves on instanton moduli spaces.ReviewsAuthor InformationRoman Bezrukavnikov, Massachusetts Institute of Technology, Cambridge, MA. Alexander Braverman, University of Toronto, ON, Canada, Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, and Skolkovo Institute for Science and Technology, Moscow, Russia. Zhiwei Yun, Yale University, New Haven, CT. Tab Content 6Author Website:Countries AvailableAll regions |
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