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Hardcover ISBN:  9781470435745 
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Hardcover ISBN:  9781470435745 
Product Code:  PCMS/24 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470442347 
Product Code:  PCMS/24.E 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 
Hardcover ISBN:  9781470435745 
eBook ISBN:  9781470442347 
Product Code:  PCMS/24.B 
List Price:  $237.00 $181.00 
MAA Member Price:  $213.30 $162.90 
AMS Member Price:  $189.60 $144.80 

Book DetailsIAS/Park City Mathematics SeriesVolume: 24; 2017; 436 ppMSC: Primary 14; 22
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 semisimple Lie algebra, and its subsequent proof by BeilinsonBernstein and BrylinskiKashiwara. 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, Ktheory, 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.
Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.

Table of Contents

Articles

Mark de Cataldo — Perverse sheaves and the topology of algebraic varieties

Xinwen Zhu — An introduction to affine Grassmannians and the geometric Satake equivalaence

Zhiwei Yun — Lectures on Springer theories and orbital intgegrals

Ngô Châu — Perverse sheaves and fundamental lemmas

Andrei Okounkov — Lectures on $K$theoretic computations in enumerative geometry

Hiraku Nakajima — Lectures on perverse sheaves on instanton moduli spaces


Additional Material

Reviews

As usual with the IAS/Park City publications, this is a timely and wellstructured set of lectures focused on a mathematical subject whose impact and interest is durable.
Felipe Zaldivar, MAA Reviews


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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 semisimple Lie algebra, and its subsequent proof by BeilinsonBernstein and BrylinskiKashiwara. 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, Ktheory, 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.
Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.

Articles

Mark de Cataldo — Perverse sheaves and the topology of algebraic varieties

Xinwen Zhu — An introduction to affine Grassmannians and the geometric Satake equivalaence

Zhiwei Yun — Lectures on Springer theories and orbital intgegrals

Ngô Châu — Perverse sheaves and fundamental lemmas

Andrei Okounkov — Lectures on $K$theoretic computations in enumerative geometry

Hiraku Nakajima — Lectures on perverse sheaves on instanton moduli spaces

As usual with the IAS/Park City publications, this is a timely and wellstructured set of lectures focused on a mathematical subject whose impact and interest is durable.
Felipe Zaldivar, MAA Reviews