Ebook: The Gelfand Mathematical Seminars, 1993–1995

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.

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Content:
Front Matter....Pages i-vi
Questions and Answers About Geometric Evolution Processes and Crystal Growth....Pages 1-9
Remarks on the Extatic Points of Plane Curves....Pages 11-22
Gibbs Measures and Quasi-Periodic Solutions for Nonlinear Hamiltonian Partial Differential Equations....Pages 23-43
Radon Transform and Functionals on the Spaces of Curves....Pages 45-73
A Unified Method for Solving Linear and Nonlinear Evolution Equations and an Application to Integrable Surfaces....Pages 75-92
Noncommutative Vieta Theorem and Symmetric Functions....Pages 93-100
Chern-Simons Classes and Cocycles on the Lie Algebra of the Gauge Group....Pages 101-122
Cycles for Asymptotic Solutions and the Weyl Group....Pages 123-150
Homology of Moduli of Curves and Commutative Homotopy Algebras....Pages 151-170
Canonical States on the Group of Automorphisms of a Homogeneous Tree....Pages 171-178
Second Quantization of the Wilson Loop....Pages 179-224
The Homogeneous Complex Monge-Amp?re Equation and the Infinite Dimensional Versions of Classic Symmetric Spaces....Pages 225-242
Novikov Inequalities for Vector Fields....Pages 243-274

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Content:
Front Matter....Pages i-vi
Questions and Answers About Geometric Evolution Processes and Crystal Growth....Pages 1-9
Remarks on the Extatic Points of Plane Curves....Pages 11-22
Gibbs Measures and Quasi-Periodic Solutions for Nonlinear Hamiltonian Partial Differential Equations....Pages 23-43
Radon Transform and Functionals on the Spaces of Curves....Pages 45-73
A Unified Method for Solving Linear and Nonlinear Evolution Equations and an Application to Integrable Surfaces....Pages 75-92
Noncommutative Vieta Theorem and Symmetric Functions....Pages 93-100
Chern-Simons Classes and Cocycles on the Lie Algebra of the Gauge Group....Pages 101-122
Cycles for Asymptotic Solutions and the Weyl Group....Pages 123-150
Homology of Moduli of Curves and Commutative Homotopy Algebras....Pages 151-170
Canonical States on the Group of Automorphisms of a Homogeneous Tree....Pages 171-178
Second Quantization of the Wilson Loop....Pages 179-224
The Homogeneous Complex Monge-Amp?re Equation and the Infinite Dimensional Versions of Classic Symmetric Spaces....Pages 225-242
Novikov Inequalities for Vector Fields....Pages 243-274
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