000			02611 a2200289 4500
003			OSt
005			20220321150717.0
008			220311b xxu||||| |||| 00| 0 eng d
020			_a9781470435745
040			_cIIT Kanpur
041			_aeng
082			_a516.35 _bG292
245			_aGeometry of moduli spaces and representation theory [Vol. 24] _cedited by Roman Bezrukavnikov, Alexander Braverman and Zhiwei Yun
260			_bAmerican Mathematical Society _aProvidence
260			_bInstitute for Advanced Study _c2017 _aNew Jersey
300			_ax, 436p
440			_aIAS/PARK CITY mathematics series
490			_a/ edited by Rafe Mazzeo; v. 24
520			_aThis 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.
650			_aModuli theory
650			_aRepresentations of algebras
650			_aGeometry, Algebraic
700			_aBezrukavnikov, Roman [ed.]
700			_aBraverman, Alexander [ed.]
700			_aYun, Zhiwei [ed.]
942			_cBK
999			_c565292 _d565292