Geometry Of Moduli Spaces And Representation Theory
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Geometry Of Moduli Spaces And Representation Theory
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Author : Roman Bezrukavnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-15
Geometry Of Moduli Spaces And Representation Theory written by Roman Bezrukavnikov 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 2017-12-15 with Mathematics categories.
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.
Geometry Of Moduli
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Author : Jan Arthur Christophersen
language : en
Publisher: Springer
Release Date : 2018-11-24
Geometry Of Moduli written by Jan Arthur Christophersen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-24 with Mathematics categories.
The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.
The Geometry Of Moduli Spaces Of Sheaves
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27
The Geometry Of Moduli Spaces Of Sheaves written by Daniel Huybrechts 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 2010-05-27 with Mathematics categories.
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Basics Of Representation Theory
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.
Geometric Representation Theory And Gauge Theory
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Author : Alexander Braverman
language : en
Publisher: Springer Nature
Release Date : 2019-11-22
Geometric Representation Theory And Gauge Theory written by Alexander Braverman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Mathematics categories.
This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.
The Moduli Space Of Curves
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Author : Robert H. Dijkgraaf
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Moduli Space Of Curves written by Robert H. Dijkgraaf 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 2012-12-06 with Mathematics categories.
This generalization of geometry is bound to have wide spread repercussions for mathematics as well as physics. The unearthing of it will entail a new golden age in the interaction of mathematics and physics. E. Witten (1986) The idea that the moduli space Mg of curves of fixed genus 9 - that is, the algebraic variety that parametrizes all curves of genus 9 - is an intriguing object in its own right seems to have come slowly. Although the para meters or moduli of curves surface in Riemann's famous memoir on abelian functions (from 1857) and in work of Hurwitz and later were considered by the geometers of the Italian school, for a long time they attracted attention only in the special case 9 = 1, where they were studied in the framework of the theory of modular functions. The work of Grothendieck, who in the early sixties pointed the way towards the right approach, and the subsequent construction (in 1965) of the moduli space Mg by Mumford were the first foundational work, to be followed by the construction of a compactification Mg by Deligne and Mumford in 1969. The theorem of Harris and Mumford saying that for 9 sufficiently large the space Mg is of general type was the first big insight in its structure.
Vertex Algebras And Algebraic Curves
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Author : Edward Frenkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-08-25
Vertex Algebras And Algebraic Curves written by Edward Frenkel 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 2004-08-25 with Mathematics categories.
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.
Moduli Spaces And Vector Bundles
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Author : Steve Bradlow
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Steve Bradlow 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 2009-05-21 with Mathematics categories.
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
The Mathematics Of Data
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Author : Michael W. Mahoney
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-11-15
The Mathematics Of Data written by Michael W. Mahoney 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 2018-11-15 with Computers categories.
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Harmonic Analysis And Applications
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Author : Carlos E. Kenig
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-14
Harmonic Analysis And Applications written by Carlos E. Kenig 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 2020-12-14 with Education categories.
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.