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

The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles
Author: Richard Wentworth
Publisher: World Scientific
Total Pages: 412
Release: 2018-06-28
Genre: Mathematics
ISBN: 9813229101

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

Moduli Spaces and Vector Bundles
Author: Steve Bradlow
Publisher: Cambridge University Press
Total Pages: 516
Release: 2009-05-21
Genre: Mathematics
ISBN: 0521734711

Coverage includes foundational material as well as current research, authored by top specialists within their fields.

The Geometry of Moduli Spaces of Sheaves

The Geometry of Moduli Spaces of Sheaves
Author: Daniel Huybrechts
Publisher: Cambridge University Press
Total Pages: 345
Release: 2010-05-27
Genre: Mathematics
ISBN: 1139485822

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.

Moduli Spaces and Vector Bundles—New Trends

Moduli Spaces and Vector Bundles—New Trends
Author: Peter Gothen
Publisher: American Mathematical Society
Total Pages: 382
Release: 2024-07-18
Genre: Mathematics
ISBN: 1470472961

This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector Bundles—New Trends, held in honor of Peter Newstead's 80th birthday, from July 25–29, 2022, at the University of Warwick, Coventry, United Kingdom. The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory, Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research articles. Most articles contain substantial background and will be helpful to both novices and experts.

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
Author: Alfonso Zamora Saiz
Publisher: Springer Nature
Total Pages: 127
Release: 2021-03-24
Genre: Mathematics
ISBN: 3030678296

This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.

Integrable Systems

Integrable Systems
Author: N.J. Hitchin
Publisher: Oxford University Press, USA
Total Pages: 148
Release: 2013-03-14
Genre: Mathematics
ISBN: 0199676771

Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles

Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles
Author: Oscar García-Prada
Publisher: American Mathematical Soc.
Total Pages: 96
Release: 2007
Genre: Mathematics
ISBN: 0821839721

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. in this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and the authors carry out a careful analysis of them by studying their variation with this parameter. Thus the authors obtain in particular information about the topology of the moduli spaces of parabolic triples for the value of the parameter relevant to the study of parabolic Higgs bundles. The remaining critical submanifolds are also described: one of them is the moduli space of parabolic bundles, while the rem

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Calabi-Yau Varieties: Arithmetic, Geometry and Physics
Author: Radu Laza
Publisher: Springer
Total Pages: 542
Release: 2015-08-27
Genre: Mathematics
ISBN: 1493928309

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.

Geometry and Physics: Volume 2

Geometry and Physics: Volume 2
Author: Jørgen Ellegaard Andersen
Publisher: Oxford University Press
Total Pages: 400
Release: 2018-10-18
Genre: Mathematics
ISBN: 019252237X

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

Topology, Geometry And Field Theory - Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference

Topology, Geometry And Field Theory - Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference
Author: Kenji Fukaya
Publisher: World Scientific
Total Pages: 266
Release: 1994-08-31
Genre:
ISBN: 9814550647

Nobel Symposium 129 on Neutrino Physics was held at Haga Slott in Enköping, Sweden during August 19-24, 2004. Invited to the symposium were around 40 globally leading researchers in the field of neutrino physics, both experimental and theoretical.The dominant theme of the lectures was neutrino oscillations, which after several years were recently verified by results from the Super-Kamiokande detector in Kamioka, Japan and the SNO detector in Sudbury, Canada. Discussion focused especially on effects of neutrino oscillations derived from the presence of matter and the fact that three different neutrinos exist. Since neutrino oscillations imply that neutrinos have mass, this is the first experimental observation that fundamentally deviates from the standard model of particle physics. This is a challenge to both theoretical and experimental physics. The various oscillation parameters will be determined with increased precision in new, specially designed experiments. Theoretical physics is working intensively to insert the knowledge that neutrinos have mass into the theoretical models that describe particle physics. The lectures provided a very good description of the intensive situation in the field right now. The topics discussed also included mass models for neutrinos, neutrinos in extra dimensions as well as the “seesaw mechanism,” which provides a good description of why neutrino masses are so small.This book is A4 size and in full color.