Manifolds and Modular Forms

Author: Friedrich Hirzebruch

Publisher: Springer-Verlag

ISBN: 3663140458

Category: Mathematics

Page: 212

View: 7729

Elliptic Curves and Modular Forms in Algebraic Topology

Proceedings of a Conference held at the Institute for Advanced Study, Princeton, Sept. 15-17, 1986

Author: Peter S. Landweber

Publisher: Springer

ISBN: 3540393005

Category: Mathematics

Page: 232

View: 3083

A small conference was held in September 1986 to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology. The resulting papers range, fom these topics through to quantum field theory, with considerable attention to formal groups, homology and cohomology theories, and circle actions on spin manifolds. Ed. Witten's rich article on the index of the Dirac operator in loop space presents a mathematical treatment of his interpretation of elliptic genera in terms of quantum field theory. A short introductory article gives an account of the growth of this area prior to the conference.

Galois Theory and Modular Forms

Author: Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamura

Publisher: Springer Science & Business Media

ISBN: 1461302498

Category: Mathematics

Page: 394

View: 8626

This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.

Topological Modular Forms

Author: Christopher L. Douglas, John Francis, André G. Henriques, Michael A. Hill

Publisher: American Mathematical Soc.

ISBN: 1470418843

Category: Mathematics

Page: 318

View: 4873

The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.

Manifolds and Geometry

Author: P. de Bartolomeis,F. Tricerri,E. Vesentini

Publisher: Cambridge University Press

ISBN: 9780521562164

Category: Mathematics

Page: 321

View: 9606

Brought together in this book are papers from a conference on differential geometry held in Pisa, in honour of Eugenio Calabi. The contributions cover a wide spectrum of areas and give an unsurpassed overview of research into differential geometry that will interest all who work in this subject.

Modular Forms and String Duality

Author: Noriko Yui, Helena Verrill, and Charles F. Doran

Publisher: American Mathematical Soc.

ISBN: 9780821871577

Category:

Page: N.A

View: 5775

Collected Works

Author: Michael Francis Atiyah

Publisher: Oxford University Press

ISBN: 9780198532774

Category: Mathematiacs--1961--

Page: 593

View: 8419

One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.

Topological Quantum Field Theory and Four Manifolds

Author: Jose Labastida,Marcos Marino

Publisher: Springer Science & Business Media

ISBN: 1402030584

Category: Science

Page: 224

View: 702

The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Quanta of Maths

Author: Alain Connes,Institut Henri Poincaré,Institut des hautes études scientifiques (Paris, France),Institut de mathématiques de Jussieu

Publisher: American Mathematical Soc.

ISBN: 0821852035

Category: Mathematics

Page: 675

View: 8533

The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.

Infinite Dimensional Groups and Manifolds

Author: Tilmann Wurzbacher

Publisher: Walter de Gruyter

ISBN: 3110200015

Category: Mathematics

Page: 256

View: 2806

Dieser Band beinhaltet eine Sammlung wissenschaftlicher Forschungsbeiträge zu unendlich-dimensionalen Gruppen und Mannigfaltigkeiten in der Mathematik und Quantenphysik.

Automorphic Forms and Lie Superalgebras

Author: Urmie Ray

Publisher: Springer Science & Business Media

ISBN: 1402050100

Category: Mathematics

Page: 278

View: 6815

This book provides the reader with the tools to understand the ongoing classification and construction project of Lie superalgebras. It presents the material in as simple terms as possible. Coverage specifically details Borcherds-Kac-Moody superalgebras. The book examines the link between the above class of Lie superalgebras and automorphic form and explains their construction from lattice vertex algebras. It also includes all necessary background information.

Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

Author: Jayce Getz,Mark Goresky

Publisher: Springer Science & Business Media

ISBN: 3034803516

Category: Mathematics

Page: 258

View: 9677

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

String-Math 2014

Author: Vincent Bouchard:,Charles Doran,Stefan Méndez-Diez,Callum Quigley

Publisher: American Mathematical Soc.

ISBN: 1470419920

Category: $K$-theory

Page: 396

View: 2647

The conference String-Math 2014 was held from June 9–13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: “String-Math Summer School” (held from June 2–6, 2014, at the University of British Columbia), “Calabi-Yau Manifolds and their Moduli” (held from June 14–18, 2014, at the University of Alberta), and “Quantum Curves and Quantum Knot Invariants” (held from June 16–20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.

Modular Forms and Galois Cohomology

Author: Haruzo Hida,Professor Haruzo Hida

Publisher: Cambridge University Press

ISBN: 9780521770361

Category: Mathematics

Page: 343

View: 5775

Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.

G-Functions and Geometry

A Publication of the Max-Planck-Institut für Mathematik, Bonn

Author: Yves André

Publisher: Springer-Verlag

ISBN: 366314108X

Category: Mathematics

Page: 232

View: 4976

The 1-2-3 of Modular Forms

Lectures at a Summer School in Nordfjordeid, Norway

Author: Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier

Publisher: Springer Science & Business Media

ISBN: 9783540741190

Category: Mathematics

Page: 266

View: 3538

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

String-Math 2013

Author: Ron Donagi, Michael R. Douglas,Ljudmila Kamenova,Martin Rocek

Publisher: American Mathematical Soc.

ISBN: 1470410516

Category: Mathematics

Page: 370

View: 2905

This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.

Standard Model and Beyond

Proceedings of the XIII International School of Theoretical Physics, Szczyrk, September 19-26 1989, University of Silesia, Katowice

Author: M. Zrałek,R. Mańka

Publisher: Nova Publishers

ISBN: 9781560720270

Category: Science

Page: 428

View: 2184

Standard Model & Beyond Proceedings Of The Xiii International School Of Theoretical Physics - Szczyrk, September 19-26 1989, University Of Silesia, Katowice