Surveys in Modern Mathematics

doi:10.1017/CBO9780511614156

This collection of articles from the Independent University of Moscow is derived from the Globus seminars held there. They are given by world authorities, from Russia and elsewhere, in various areas of mathematics and are designed to introduce graduate students to some of the most dynamic areas of mathematical research. The seminars aim to be informal, wide-ranging and forward-looking, getting across the ideas and concepts rather than formal proofs, and this carries over to the articles here. Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups. The volume as a whole is a fascinating and exciting overview of contemporary mathematics.

‘… a fascinating and exciting overview of contemporary mathematics.‘

Source: L'Enseignement Mathématique

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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The Independent University of Moscow and Student Sessions at the IUM
pp vii-xii
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Mysterious mathematical trinities
pp 1-12
- By V. I. Arnold
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The principle of topological economy in algebraic geometry
pp 13-23
- By V. I. Arnold
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Rational curves, elliptic curves, and the Painlevé equation
pp 24-33
- By Yu. I. Manin
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The orbit method and finite groups
pp 34-69
- By A. A. Kirillov
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On the development of the theory of dynamical systems during the past quarter century
pp 70-185
- By D. V. Anosov
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Foundations of computational complexity theory
pp 186-202
- By A. A. Razborov
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The Schrödinger equation and symplectic geometry
pp 203-210
- By S. P. Novikov
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Rings and algebraic varieties
pp 211-215
- By Miles Reid
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Billiard table as a playground for a mathematician
pp 216-242
- By A. B. Katok
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The Fibonacci numbers and simplicity of 2127 – 1
pp 243-254
- By A. N. Rudakov
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On problems of computational complexity
pp 255-259
- By Stephen Smale
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Values of the ζ-function
pp 260-273
- By Pierre Cartier
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Combinatorics of trees
pp 274-282
- By Pierre Cartier
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What is an operad?
pp 283-291
- By Pierre Cartier
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The orbit method beyond Lie groups. Infinite-dimensional groups
pp 292-304
- By A. A. Kirillov
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The orbit method beyond Lie groups. Quantum groups
pp 305-315
- By A. A. Kirillov
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Conformal mappings and the Whitham equations
pp 316-327
- By I. M. Krichever
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Projective differential geometry: old and new
pp 328-337
- By V. Yu. Ovsienko
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Haken's method of normal surfaces and its applications to classification problem for 3-dimensional manifolds – the life story of one theorem
pp 338-348
- By S. V. Matveev
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Surveys in Modern Mathematics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

The Independent University of Moscow and Student Sessions at the IUM
pp vii-xii

Mysterious mathematical trinities
pp 1-12

The principle of topological economy in algebraic geometry
pp 13-23

Rational curves, elliptic curves, and the Painlevé equation
pp 24-33

The orbit method and finite groups
pp 34-69

On the development of the theory of dynamical systems during the past quarter century
pp 70-185

Foundations of computational complexity theory
pp 186-202

The Schrödinger equation and symplectic geometry
pp 203-210

Rings and algebraic varieties
pp 211-215

Billiard table as a playground for a mathematician
pp 216-242

The Fibonacci numbers and simplicity of 2127 – 1
pp 243-254

On problems of computational complexity
pp 255-259

Values of the ζ-function
pp 260-273

Combinatorics of trees
pp 274-282

What is an operad?
pp 283-291

The orbit method beyond Lie groups. Infinite-dimensional groups
pp 292-304

The orbit method beyond Lie groups. Quantum groups
pp 305-315

Conformal mappings and the Whitham equations
pp 316-327

Projective differential geometry: old and new
pp 328-337

Haken's method of normal surfaces and its applications to classification problem for 3-dimensional manifolds – the life story of one theorem
pp 338-348

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Surveys in Modern Mathematics

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