Mumford Tate Groups And Domains
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Mumford Tate Groups And Domains
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Author : Mark Green
language : en
Publisher: Princeton University Press
Release Date : 2012-04-22
Mumford Tate Groups And Domains written by Mark Green and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-22 with Mathematics categories.
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
Mumford Tate Groups And Domains
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Author : Mark Green
language : en
Publisher: Annals of Mathematics Studies
Release Date : 2012
Mumford Tate Groups And Domains written by Mark Green and has been published by Annals of Mathematics Studies this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
Mumford Tate Groups And Domains
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Author : Mark Green
language : en
Publisher: Princeton University Press
Release Date : 2012-04-22
Mumford Tate Groups And Domains written by Mark Green and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-22 with Mathematics categories.
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
Period Mappings And Period Domains
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Author : James Carlson
language : en
Publisher: Cambridge University Press
Release Date : 2017-08-24
Period Mappings And Period Domains written by James Carlson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-24 with Mathematics categories.
An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.
Hodge Theory Complex Geometry And Representation Theory
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Author : Mark Green
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-11-05
Hodge Theory Complex Geometry And Representation Theory written by Mark Green and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-05 with Mathematics categories.
This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.
Recent Advances In Hodge Theory
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Author : Matt Kerr
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-04
Recent Advances In Hodge Theory written by Matt Kerr and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-04 with Mathematics categories.
Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
Calabi Yau Varieties Arithmetic Geometry And Physics
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Author : Radu Laza
language : en
Publisher: Springer
Release Date : 2015-08-27
Calabi Yau Varieties Arithmetic Geometry And Physics written by Radu Laza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Mathematics categories.
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.
The Abel Prize 2008 2012
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-21
The Abel Prize 2008 2012 written by Helge Holden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-21 with Mathematics categories.
Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners.
Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces
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Author : Marc-Hubert Nicole
language : en
Publisher: Springer Nature
Release Date : 2020-10-31
Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces written by Marc-Hubert Nicole and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-31 with Mathematics categories.
This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures; A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective; A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case; An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties. Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.
Special Values Of Automorphic Cohomology Classes
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Author : Mark Green
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12
Special Values Of Automorphic Cohomology Classes written by Mark Green and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Mathematics categories.
The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.