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1990-1992 : us ISBN 9780817636890
内容説明
This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organize their publication before 1990. Since 1990, most of the talks have taken place at Rutgers University in New Brunswick, New Jersey. Parallel seminars were also held in Moscow, and during July, 1992, at IRES in Bures-sur-Yvette, France. Speakers were invited to submit papers in their own style, and to elaborate on what they discussed in the Seminar. We hope that readers will find the diversity of styles appealing, and recognize that to some extent this reflects the diversity of styles in a mathematical society. The principal aim was to have interesting talks, even if the topic was not especially popular at the time. The papers listed in the Table of Contents reflect some of the rich variety of ideas presented in the Seminar. Not all the speakers submit ted papers. Among the interesting talks that influenced the seminar in an important way, let us mention, for example, that of R. Langlands on per colation theory and those of J. Conway and J. McKay on sporadic groups. In addition, there were many extemporaneous talks as well as short discus sions.
目次
The Degeneracy of Two Spectral Sequences.- Hopf Algebra Structures for the Heisenberg Algebra: I.- Avalanches, Sandpiles and Tutte Decompositions.- On the Dimension and Degree of the Projective Dual Variety: A q-Analog of the Katz-Kleiman Formula.- Crofton Densities and Nonlocal Differentials.- On the Local Geometry of a Bihamiltonian Structure.- The Classical Polylogarithms, Algebraic K-Theory and ?F(N).- A Brief History of the Sporadic Simple Groups.- Vertex Operator Algebras and Operads.- Representations of the Quantized Function Algebras, 2-Categories and Zamolodchikov Tetrahedra Equation.- Formal (Non)-Commutative Symplectic Geometry.- Constructible Functions, Lagrangian Cycles and Computational Geometry.- Quantum Groups and Perverse Sheaves. An Example.- Linearly Recursive Sequences, Witt Algebras and Quantum Groups.- Complexes of Connected Graphs.
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1993-1995 : us ISBN 9780817638160
内容説明
The Seminar has taken place at Rutgers University in New Brunswick, New Jersey, since 1990 and it has become a tradition, starting in 1992, that the Seminar be held during July at IHES in Bures-sur-Yvette, France. This is the second Gelfand Seminar volume published by Birkhauser, the first having covered the years 1990-1992. Most of the papers in this volume result from Seminar talks at Rutgers, and some from talks at IHES. In the case of a few of the papers the authors did not attend, but the papers are in the spirit of the Seminar. This is true in particular of V. Arnold's paper. He has been connected with the Seminar for so many years that his paper is very natural in this volume, and we are happy to have it included here. We hope that many people will find something of interest to them in the special diversity of topics and the uniqueness of spirit represented here. The publication of this volume would be impossible without the devoted attention of Ann Kostant. We are extremely grateful to her. I. Gelfand J. Lepowsky M. Smirnov Questions and Answers About Geometric Evolution Processes and Crystal Growth Fred Almgren We discuss evolutions of solids driven by boundary curvatures and crystal growth with Gibbs-Thomson curvature effects. Geometric measure theo retic techniques apply both to smooth elliptic surface energies and to non differentiable crystalline surface energies.
目次
Questions and Answers about Geometric Evolution Processes and Crystal Growth.- Remarks on the Extatic Points of Plane Curves.- Gibbs Measures and Quasi-Periodic Solutions for Nonlinear Hamiltonian Partial Differential Equations.- Radon Transform and Functionals on the Spaces of Curves.- A Unified Method for Solving Linear and Nonlinear Evolution Equations and an Application to Integrable Surfaces.- Noncommutative Vieta Theorem and Symmetric Functions.- Chern-Simons Classes and Cocycles on the Lie Algebra of the Gauge Group.- Cycles for Asymptotic Solutions and the Weyl Group.- Homology of Moduli of Curves and Commutative Homotopy Algebras.- Canonical States on the Group of Automorphisms of a Homogeneous Tree.- Second Quantization of the Wilson Loop.- The Homogeneous Complex Monge-Ampere Equation and the Infinite Dimensional Versions of Classic Symmetric Spaces.- Novikov Inequalities for Vector Fields.
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1996-1999 : us ISBN 9780817640132
内容説明
Dedicated to the memory of Chih-Han Sah, this volume covers a number of topics, including: combinatorial geometry, connections between logic and geometry, Lie groups, algebras and their representations, and non-communcative algebra and its relations to physics.
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1990-1992 : gw ISBN 9783764336899
内容説明
The world famous Gelfand Seminars began in Moscow in November 1943 and have continued uninterrupted to the present time, having recently moved their location to Rutgers University in New Brunswick, New Jersey. Parallel seminars have also been held in Moscow during July 1992, and at the IHES in Bures-sur-Yvette, France. The Seminars have always been known for their breadth of topics and diversity of styles - a true globalization of the art and science of mathematics. Many renowned mathematicians have presented new and interesting ideas at these seminars and been challenged and stimulated by the lively interaction with their colleagues and graduate students. Among the mathematicians represented in the 1990-1992 Seminars are: Jean-Luc Brylinski L. Corwin A. M. Gabrielov 1. M. Gelfand B. Goncharov D. Gorenstein Y.-Z. Huang M. M. Kapranov D. Kazhdan
目次
Preface I.M. Gelfand The Degeneracy of Two Spectral Sequences Jean-Luc Brylinski Hopf Algebra Structures for the Heisenberg Algebra: I L. Corwin and I. M. Gelfand Avalanches, Sandpiles and Tutte Decompositions A. Gabrielov On the Dimension and Degree of the Projective Dual Variety: A q-Analog of the Katz-Kleiman Formula I. M. Gelfand and M. M. Kapranov Nonlocal Differentials I. M. Gelfand and M. M. Smirnov On the Local Geometry of a Bihamiltonian Structure 1. M. Gelfand and I. Zakharevich The classical polylogarithms, algebraic K-theory and CF(n) A. B. Goncharov A brief history of the sporadic simple groups Daniel Gorenstein Representations of the quantized function algebra's 2-categories and Zarnoladchikov tetrahedra equation D. Kazhdan and Y. Soibelman Formal (Non)-Commutative Symplectic Geometry Maxim Kontsevich Vertex operator algebras and operads Y-Zhi Huang and James Lepowsky Constructible functions, Lagrangian cycles and Computational Geometry Pierre Schapira Quantum groups and perverse sheaves. An example Vadim Schechtman Linearly Recursive Sequences, Witt Algebras and Quantum Groups E. J. Taft Complexes of Connected Graphs V. A. Vassiliev
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1993-1995 : gw ISBN 9783764338169
内容説明
Part of a series of texts taken from the weekly seminars held at Rutgers University. The topics are diverse, coming from many fields of mathematics and stressing a global view of mathematics and science.
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1996-1999 : gw ISBN 9783764340131
内容説明
Dedicated to the memory of Chih-Han Sah, this volume covers a number of topics, including: combinatorial geometry, connections between logic and geometry, Lie groups, algebras and their representations, and non-communcative algebra and its relations to physics.
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