An Introduction to Invariants and Moduli

Author: Shigeru Mukai,Mukai Shigeru

Publisher: Cambridge University Press

ISBN: 9780521809061

Category: Mathematics

Page: 503

View: 1511

Incorporated in this volume are the first two books in Mukai's series on Moduli Theory. The notion of a moduli space is central to geometry. However, it's influence is not confined there; for example the theory of moduli spaces is a crucial ingredient in the proof of Fermat's last theorem. An accurate account of Mukai's influential Japanese texts, this tranlation will be a valuable resource for researchers and graduate students working in a range of areas.

Trends in Representation Theory of Algebras and Related Topics

Author: Andrzej Skowroński

Publisher: European Mathematical Society

ISBN: 9783037190623

Category: Mathematics

Page: 710

View: 1152

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatories, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development.

Developments and Retrospectives in Lie Theory

Algebraic Methods

Author: Geoffrey Mason,Ivan Penkov,Joseph A. Wolf

Publisher: Springer

ISBN: 3319098047

Category: Mathematics

Page: 397

View: 5458

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Cohomological and Geometric Approaches to Rationality Problems

New Perspectives

Author: Fedor Bogomolov,Yuri Tschinkel

Publisher: Springer Science & Business Media

ISBN: 9780817649340

Category: Mathematics

Page: 314

View: 7571

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov

The Geometry and Physics of Knots

Author: Michael Francis Atiyah

Publisher: Cambridge University Press

ISBN: 9780521395540

Category: Mathematics

Page: 78

View: 4701

Deals with an area of research that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

Winter School on Mirror Symmetry, Vector Bundles, and Lagrangian Submanifolds

Proceedings of the Winter School on Mirror Symmetry, January 1999, Harvard University, Cambridge, Massachusetts

Author: Cumrun Vafa

Publisher: American Mathematical Soc.

ISBN: 9780821821596

Category: Mathematics

Page: 377

View: 4046

The collection of articles in this volume are based on l ectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many new directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics. This book brings together the latest research in a major area of mathematical physics, including the recent progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included. Other AMS titles edited by S.-T Yau published in the AMS/IP Studies in Advanced Mathematics series include, Mirror Symmetry III, Volume 10, Mirror symmetry II, Volume 1, and Mirror Symmetry I, Volume 9.

Topics in Metric Fixed Point Theory

Author: Kazimierz Goebel,W. A. Kirk

Publisher: Cambridge University Press

ISBN: 9780521382892

Category: Mathematics

Page: 244

View: 9198

Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.

Geometrische Methoden in der Invariantentheorie

Author: Hanspeter Kraft

Publisher: Springer-Verlag

ISBN: 3663101436

Category: Technology & Engineering

Page: 308

View: 2889

In dieser Einführung geht es vor allem um die geometrischen Aspekte der Invariantentheorie. Die hauptsächliche Motivation bildet das Studium von Klassifikations- und Normalformenproblemen, die auch historisch der Ausgangspunkt für invariantentheoretische Untersuchungen waren.

Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces

Mumbai 2004

Author: V. B. Mehta

Publisher: N.A

ISBN: 9788173198021

Category: Mathematics

Page: 543

View: 1892

The area of Algebraic Groups and Homogeneous Spaces is one area in which major advances have been made in recent decades. This volume contains articles by several leading experts in central topics in the area, including representation theory in characteristic p, combinatorial representation theory, flag varieties, Schubert varieties, vector bundles, loop groups and Kac-Moody Lie algebras, Galois cohomology of algebraic groups, and Tannakian categories. In addition to original papers in these areas, the volume includes a survey on representation theory in characteristic p by H. Andersen and an article by T.A. Springer on Armand Borel's work in algebraic groups and Lie groups.

Ebene algebraische Kurven

Author: Egbert Brieskorn,Horst Knörrer

Publisher: N.A


Category: Mathematics

Page: 964

View: 1057


An Introduction to Continuum Mechanics

Author: J. N. Reddy

Publisher: Cambridge University Press

ISBN: 1107292409

Category: Science

Page: N.A

View: 6434

This best-selling textbook presents the concepts of continuum mechanics in a simple yet rigorous manner. It introduces the invariant form as well as the component form of the basic equations and their applications to problems in elasticity, fluid mechanics and heat transfer, and offers a brief introduction to linear viscoelasticity. The book is ideal for advanced undergraduates and graduate students looking to gain a strong background in the basic principles common to all major engineering fields, and for those who will pursue further work in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary areas such as geomechanics, biomechanics, mechanobiology and nanoscience. The book features derivations of the basic equations of mechanics in invariant (vector and tensor) form and specification of the governing equations to various co-ordinate systems, and numerous illustrative examples, chapter summaries and exercise problems. This second edition includes additional explanations, examples and problems.


Author: Hubert Brian Griffiths

Publisher: N.A


Category: Surfaces

Page: 147

View: 8532


Algebraische Transformationsgruppen und Invariantentheorie Algebraic Transformation Groups and Invariant Theory

Author: Hanspeter Kraft,Slodowy

Publisher: Birkhäuser

ISBN: 9783764322847

Category: Mathematics

Page: 214

View: 8719

Der. vorliegende Band enthält eine Reihe von einführenden Vorlesungen, die von verschiedenen Autoren im Rahmen von zwei DMV-Seminaren zum Thema "Algebraische Transjormationsgruppen und Invariantentheorie" gehalten wur den. Entsprechend der allgemeinen Zielsetzung der DMV-Seminare sollten sowohl grundlegende Techniken und Resultate vorgestellt als auch Einblicke in aktuelle Entwickl~ngen gegeben werden. Was die Grundlagen anbetrifft, so haben wir sie hier nicht in vollem Umfang widergegeben. Im Bedarfsfall mag der Leser unsere Bücher "Geometrische Methoden in der Invariantentheorie"l und "Invariant Theory"2 zu Rate ziehen, auf die sich die einführenden Vorträge stützten. Leider konnten auch nicht alle aktuellen Entwicklungen berücksichtigt werden, über die im Seminar berichtet wurde. Die Ziele der hier vorliegenden Beiträge, auf deren Inhalt wir in der Einführung ausführlicher eingehen werden, sind entsprechend unterschiedlicher Natur. Einige liefern Darstellungen bereits publizierter Theorien, wobei sie allerdings ein größeres Gewicht auf Motivation und die Ausführung von Beispie len legen, als dies in den Originalarbeiten möglich war. Andere leiten grundle gende Resultate auf neue "reise her oder stellen sie aus anderer Sicht dar. Schließlich werden auch noch einzelne Einblicke in aktuelle Forschungsrichtun gen gegeben. Wir hoffen, daß durch diesen Band zahlreiche Resultate der Theorie der algebraischen Transformationsgruppen leichter zugänglich geworden sind, und daß der Leser mit ihm eine nützliche Basis für die Lektüre aktueller Forschungsarbeiten erhält.

Formes Automorphes (I)

Actes Du Semestre Du Centre Émile Borel, Printemps 2000

Author: Jacques Tilouine

Publisher: N.A

ISBN: 9782856291726

Category: Automorphic forms

Page: 410

View: 5021

Ce volume est le premier d'une série de deux consacrés aux formes automorphes sous leurs aspects géométrique et arithmétique et à certains points du programme de Langlands. Les thèmes abordés dans ce volume concernent les formes modulaires p-adiques, la correspondance locale de Langlands pour GL(n), la cohomologie des variétés de Shimura, leur réduction modulo p et leurs stratifications associées aux polygones de Newton.

Number theory

New York seminar 1989-1990

Author: David Chudnovsky

Publisher: Springer Verlag

ISBN: 9780387976709

Category: Mathematics

Page: 275

View: 1790

This is a volume of papers presented at the New York Number Theory Seminar. Since 1982, the Seminar has been meeting weekly during the academic year at the Graduate School and University Center of the City University of New York. This collection of papers covers a wide area of number theory, particularly modular functions, algebraic and diophantine geometry, and computational number theory.