Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces
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Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces
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Author : William Mark Goldman
language : en
Publisher:
Release Date : 2008
Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces written by William Mark Goldman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Geometry, Algebraic categories.
Details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. This work constructs an equivalence between the deformation theories of flat connections and Higgs pairs, providing an identification of moduli spaces arising in different contexts.
Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces
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Author : William Mark Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces written by William Mark Goldman 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 2008 with Mathematics categories.
This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkähler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.
Problems On Mapping Class Groups And Related Topics
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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-09-12
Problems On Mapping Class Groups And Related Topics written by Benson Farb 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 2006-09-12 with Mathematics categories.
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Geometry And Physics Volume 2
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Author : Jørgen Ellegaard Andersen
language : en
Publisher: Oxford University Press
Release Date : 2018-10-18
Geometry And Physics Volume 2 written by Jørgen Ellegaard Andersen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Mathematics categories.
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.
Geometry And Physics
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Author : Jørgen Ellegaard Andersen
language : en
Publisher: Oxford University Press, USA
Release Date : 2018
Geometry And Physics written by Jørgen Ellegaard Andersen and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
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.
The Many Facets Of Geometry
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Author : Oscar Garcia-Prada
language : en
Publisher: OUP Oxford
Release Date : 2010-07-01
The Many Facets Of Geometry written by Oscar Garcia-Prada and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
Few people have proved more influential in the field of differential and algebraic geometry, and in showing how this links with mathematical physics, than Nigel Hitchin. Oxford University's Savilian Professor of Geometry has made fundamental contributions in areas as diverse as: spin geometry, instanton and monopole equations, twistor theory, symplectic geometry of moduli spaces, integrables systems, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, special Lagrangian geometry and mirror symmetry, theory of grebes, and many more. He was previously Rouse Ball Professor of Mathematics at Cambridge University, as well as Professor of Mathematics at the University of Warwick, is a Fellow of the Royal Society and has been the President of the London Mathematical Society. The chapters in this fascinating volume, written by some of the greats in their fields (including four Fields Medalists), show how Hitchin's ideas have impacted on a wide variety of subjects. The book grew out of the Geometry Conference in Honour of Nigel Hitchin, held in Madrid, with some additional contributions, and should be required reading for anyone seeking insights into the overlap between geometry and physics.
Geometry Topology And Dynamics Of Character Varieties
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Author : William Goldman
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Topology And Dynamics Of Character Varieties written by William Goldman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.
Vertex Operator Algebras Number Theory And Related Topics
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Author : Matthew Krauel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-13
Vertex Operator Algebras Number Theory And Related Topics written by Matthew Krauel 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 2020-07-13 with Education categories.
This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.
Complicial Sets Characterising The Simplicial Nerves Of Strict Omega Categories
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Author : Dominic Verity
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Complicial Sets Characterising The Simplicial Nerves Of Strict Omega Categories written by Dominic Verity 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 2008 with Mathematics categories.
The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title (circa 1978). On the way the author substantially develops Roberts' theory of complicial sets itself and makes contributions to Street's theory of parity complexes. In particular, he studies a new monoidal closed structure on the category of complicial sets which he shows to be the appropriate generalisation of the (lax) Gray tensor product of 2-categories to this context. Under Street's $\omega$-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.
Torus Fibrations Gerbes And Duality
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Author : Ron Donagi
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Torus Fibrations Gerbes And Duality written by Ron Donagi 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 2008 with Mathematics categories.
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form