Geometry of Moduli Spaces and Representation Theory is popular PDF and ePub book, written by Roman Bezrukavnikov in 2017-12-15, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Geometry of Moduli Spaces and Representation Theory can be Read Online from any device for your convenience.
Geometry of Moduli Spaces and Representation Theory Book PDF Summary
This 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.
Detail Book of Geometry of Moduli Spaces and Representation Theory PDF
- Author : Roman Bezrukavnikov
- Release : 15 December 2017
- Publisher : American Mathematical Soc.
- ISBN : 9781470435745
- Genre : Mathematics
- Total Page : 449 pages
- Language : English
- PDF File Size : 19,7 Mb
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