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Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 180; 1997; 255 ppMSC: Primary 57; 58; Secondary 00;
“We were fortunate. We studied under Arnold. We moved in his orbit and had the opportunity to discuss with him everything under the sun. For every one of us this was a rare gift, a great good fortune in our lives.”
—from the Introduction
Leading mathematician and expert teacher, V. I. Arnold turned 60 in June of 1997. This volume contains a selection of original papers prepared for the occasion of this 60th anniversary by former students and other participants in Arnold's Moscow seminar. A weekly event since the mid1960s, this seminar and its participants have been inspired by Arnold's creative ideas and universal approach to mathematics.
The papers in this volume reflect Arnold's wide range of interests and his scientific contributions, including singularity theory, symplectic and contact geometry, mathematical physics, and dynamical systems. The spirit of this work is consistent with Arnold's view of mathematics, connecting different areas of mathematics and theoretical physics. The book is rich in applications and geometrical in nature.ReadershipGraduate students, research mathematicians and theoretical physicists interested in singularity theory, symplectic and contact geometry, topological field theory and dynamical systems.

Table of Contents

Cover

Frontispiece

Title page

Copyright page

Contents

Preface

On the geometry of caustics

Lagrangian embeddings and Lagrangian cobordism

Polynomial invariants of Legendrian links and plane fronts

Solutions of the elliptic qKZB equations and Bethe ansatz I

Singular deformations of Lie algebras. Example: Deformations of the Lie algebra 𝐿₁

On imaginary plane curves and spin quotients of complex surfaces by complex conjugation

Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture

On a problem of B. Teissier

Embedding theorems for local maps, slowfast systems and bifurcation from MorseSmale to SmaleWilliams

Topological invariants of fiber singularities

Informal complexification and Poisson structures on moduli spaces

Consistent partitions of polytopes and polynomial measures

On primitive elements in the bialgebra of chord diagrams

Spaces of meromorphic functions on Riemann surfaces

Hamiltonian loops and Arnold’s principle

Singularities in the presence of symmetries

Discrete versions of the fourvertex theorem

Excitation of elliptic normal modes of invariant tori in Hamiltonian systems

Ramified coverings of 𝑆² with one degenerate branching point and enumeration of edgeordered graphs

On zeros of the Schwarzian derivative

Stratified PicardLefschetz theory with twisted coefficients

Back Cover


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“We were fortunate. We studied under Arnold. We moved in his orbit and had the opportunity to discuss with him everything under the sun. For every one of us this was a rare gift, a great good fortune in our lives.”
—from the Introduction
Leading mathematician and expert teacher, V. I. Arnold turned 60 in June of 1997. This volume contains a selection of original papers prepared for the occasion of this 60th anniversary by former students and other participants in Arnold's Moscow seminar. A weekly event since the mid1960s, this seminar and its participants have been inspired by Arnold's creative ideas and universal approach to mathematics.
The papers in this volume reflect Arnold's wide range of interests and his scientific contributions, including singularity theory, symplectic and contact geometry, mathematical physics, and dynamical systems. The spirit of this work is consistent with Arnold's view of mathematics, connecting different areas of mathematics and theoretical physics. The book is rich in applications and geometrical in nature.
Graduate students, research mathematicians and theoretical physicists interested in singularity theory, symplectic and contact geometry, topological field theory and dynamical systems.

Cover

Frontispiece

Title page

Copyright page

Contents

Preface

On the geometry of caustics

Lagrangian embeddings and Lagrangian cobordism

Polynomial invariants of Legendrian links and plane fronts

Solutions of the elliptic qKZB equations and Bethe ansatz I

Singular deformations of Lie algebras. Example: Deformations of the Lie algebra 𝐿₁

On imaginary plane curves and spin quotients of complex surfaces by complex conjugation

Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture

On a problem of B. Teissier

Embedding theorems for local maps, slowfast systems and bifurcation from MorseSmale to SmaleWilliams

Topological invariants of fiber singularities

Informal complexification and Poisson structures on moduli spaces

Consistent partitions of polytopes and polynomial measures

On primitive elements in the bialgebra of chord diagrams

Spaces of meromorphic functions on Riemann surfaces

Hamiltonian loops and Arnold’s principle

Singularities in the presence of symmetries

Discrete versions of the fourvertex theorem

Excitation of elliptic normal modes of invariant tori in Hamiltonian systems

Ramified coverings of 𝑆² with one degenerate branching point and enumeration of edgeordered graphs

On zeros of the Schwarzian derivative

Stratified PicardLefschetz theory with twisted coefficients

Back Cover