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Topics in Singularity Theory: V. I. Arnold’s 60th Anniversary Collection

Edited by: A. Khovanskiĭ University of Toronto, ON, Canada
A. Varchenko University of North Carolina, Chapel Hill
V. Vassiliev Steklov Mathematical Institute, Moscow, Russia
Available Formats:
Hardcover ISBN: 978-0-8218-0807-8
Product Code: TRANS2/180
255 pp
List Price: $121.00 MAA Member Price:$108.90
AMS Member Price: $96.80 Electronic ISBN: 978-1-4704-3391-8 Product Code: TRANS2/180.E 255 pp List Price:$114.00
MAA Member Price: $102.60 AMS Member Price:$91.20
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List Price: $181.50 MAA Member Price:$163.35
AMS Member Price: $145.20 Click above image for expanded view Topics in Singularity Theory: V. I. Arnold’s 60th Anniversary Collection Edited by: A. Khovanskiĭ University of Toronto, ON, Canada A. Varchenko University of North Carolina, Chapel Hill V. Vassiliev Steklov Mathematical Institute, Moscow, Russia Available Formats:  Hardcover ISBN: 978-0-8218-0807-8 Product Code: TRANS2/180 255 pp  List Price:$121.00 MAA Member Price: $108.90 AMS Member Price:$96.80
 Electronic ISBN: 978-1-4704-3391-8 Product Code: TRANS2/180.E 255 pp
 List Price: $114.00 MAA Member Price:$102.60 AMS Member Price: $91.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$181.50
MAA Member Price: $163.35 AMS Member Price:$145.20
• Book Details

American Mathematical Society Translations - Series 2
Volume: 1801997
MSC: 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 mid-1960s, 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
• 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, slow-fast systems and bifurcation from Morse-Smale to Smale-Williams
• 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 four-vertex theorem
• Excitation of elliptic normal modes of invariant tori in Hamiltonian systems
• Ramified coverings of 𝑆² with one degenerate branching point and enumeration of edge-ordered graphs
• On zeros of the Schwarzian derivative
• Stratified Picard-Lefschetz theory with twisted coefficients
• Back Cover
• Request Review Copy
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Volume: 1801997
MSC: 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 mid-1960s, 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
• 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, slow-fast systems and bifurcation from Morse-Smale to Smale-Williams
• 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 four-vertex theorem
• Excitation of elliptic normal modes of invariant tori in Hamiltonian systems
• Ramified coverings of 𝑆² with one degenerate branching point and enumeration of edge-ordered graphs
• On zeros of the Schwarzian derivative
• Stratified Picard-Lefschetz theory with twisted coefficients
• Back Cover
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