The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles

Author: B. Brent Gordon

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 631

ISBN-13: 9401140987

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The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic ipants. In addition, participants' reprints and preprints were displayed through out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction.


The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles

Author: B. Brent Gordon

Publisher:

Published: 2000

Total Pages: 432

ISBN-13: 9781470439385

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The NATO ASI/CRM Summer School at Banff offered a unique, full, and in-depth account of the topic, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods. As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to developments such as a.


The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles

Author: B. Brent Gordon

Publisher: American Mathematical Soc.

Published: 2000-01-01

Total Pages: 468

ISBN-13: 9780821870204

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From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.


Hodge Theory, Complex Geometry, and Representation Theory

Hodge Theory, Complex Geometry, and Representation Theory

Author: Robert S. Doran

Publisher: American Mathematical Soc.

Published: 2014

Total Pages: 330

ISBN-13: 0821894153

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Contains carefully written expository and research articles. Expository papers include discussions of Noether-Lefschetz theory, algebraicity of Hodge loci, and the representation theory of SL2(R). Research articles concern the Hodge conjecture, Harish-Chandra modules, mirror symmetry, Hodge representations of Q-algebraic groups, and compactifications, distributions, and quotients of period domains.


Differential Geometry and Mathematical Physics

Differential Geometry and Mathematical Physics

Author: Gerd Rudolph

Publisher: Springer

Published: 2017-03-22

Total Pages: 837

ISBN-13: 9402409599

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The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.


Recent Advances in Hodge Theory

Recent Advances in Hodge Theory

Author: Matt Kerr

Publisher: Cambridge University Press

Published: 2016-02-04

Total Pages: 533

ISBN-13: 110754629X

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Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.