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The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles

2018-06-28 Mathematics
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Release : 2018-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 101/5 ( reviews)

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Book Synopsis The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by : Richard Wentworth

Download or read book The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles written by Richard Wentworth. This book was released on 2018-06-28. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.

Moduli Spaces and Vector Bundles

2009-05-21 Mathematics
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Release : 2009-05-21
Genre : Mathematics
Kind : eBook
Book Rating : 049/5 ( reviews)

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Book Synopsis Moduli Spaces and Vector Bundles by : Leticia Brambila-Paz

Download or read book Moduli Spaces and Vector Bundles written by Leticia Brambila-Paz. This book was released on 2009-05-21. Available in PDF, EPUB and Kindle. Book excerpt: Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.

Moduli Spaces

2014-03-13 Mathematics
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Release : 2014-03-13
Genre : Mathematics
Kind : eBook
Book Rating : 194/5 ( reviews)

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Book Synopsis Moduli Spaces by : Leticia Brambila-Paz

Download or read book Moduli Spaces written by Leticia Brambila-Paz. This book was released on 2014-03-13. Available in PDF, EPUB and Kindle. Book excerpt: Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. First formalised in the 1960s, it represents a significant topic of modern mathematical research with strong connections to many areas of mathematics (including geometry, topology and number theory) and other disciplines such as theoretical physics. This book, which arose from a programme at the Isaac Newton Institute in Cambridge, is an ideal way for graduate students and more experienced researchers to become acquainted with the wealth of ideas and problems in moduli theory and related areas. The reader will find articles on both fundamental material and cutting-edge research topics, such as: algebraic stacks; BPS states and the P = W conjecture; stability conditions; derived differential geometry; and counting curves in algebraic varieties, all written by leading experts.

Geometry, Topology and Physics

2018-10-03 Mathematics
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Release : 2018-10-03
Genre : Mathematics
Kind : eBook
Book Rating : 948/5 ( reviews)

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Book Synopsis Geometry, Topology and Physics by : Mikio Nakahara

Download or read book Geometry, Topology and Physics written by Mikio Nakahara. This book was released on 2018-10-03. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Geometry of Moduli Spaces and Representation Theory

2017-12-15 Mathematics
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Release : 2017-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 748/5 ( reviews)

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Book Synopsis Geometry of Moduli Spaces and Representation Theory by : Roman Bezrukavnikov

Download or read book Geometry of Moduli Spaces and Representation Theory written by Roman Bezrukavnikov. This book was released on 2017-12-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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