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Advances in the Mathematical Sciences
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, and V. Vassiliev, Steklov Mathematical Institute, Moscow, Russia
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American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
1997; 255 pp; hardcover
Volume: 180
ISBN-10: 0-8218-0807-9
ISBN-13: 978-0-8218-0807-8
List Price: US$108
Member Price: US$86.40
Order Code: TRANS2/180
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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 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.

Readership

Graduate students, research mathematicians and theoretical physicists interested in singularity theory, symplectic and contact geometry, topological field theory and dynamical systems.

Table of Contents

  • J. W. Bruce and V. M. Zakalyukin -- On the geometry of caustics
  • Yu. V. Chekanov -- Lagrangian embeddings and Lagrangian cobordism
  • S. Chmutov and V. Goryunov -- Polynomial invariants of Legendrian links and plane fronts
  • G. Felder, V. Tarasov, and A. Varchenko -- Solutions of the elliptic qKZB equations and Bethe ansatz I
  • A. Fialowski and D. Fuchs -- Singular deformations of Lie algebras. Example: Deformations of the Lie algebra \(L_1\)
  • S. Finashin and E. Shustin -- On imaginary plane curves and spin quotients of complex surfaces by complex conjugation
  • A. Givental -- Stationary phase integrals, quantum toda lattices, flag manifolds and the mirror conjecture
  • S. M. Gusein-Zade -- On a problem of B. Teissier
  • Yu. Ilyashenko -- Embedding theorems for local maps, slow-fast systems and bifurcation from Morse-Smale to Smale-Williams
  • M. Kazaryan -- Topological invariants of fiber singularities
  • B. A. Khesin -- Informal complexification and Poisson structures on moduli spaces
  • A. Khovanskiĭ -- Consistent partitions of polytopes and polynomial measures
  • S. K. Lando -- On primitive elements in the bialgebra of chord diagrams
  • S. M. Natanzon -- Spaces of meromorphic functions on Riemann surfaces
  • L. Polterovich -- Hamiltonian loops and Arnold's principle
  • I. Scherbak -- Singularities in the presence of symmetries
  • V. D. Sedykh -- Discrete versions of the four-vertex theorem
  • M. B. Sevryuk -- Excitation of elliptic normal modes of invariant tori in Hamiltonian systems
  • B. Shapiro, M. Shapiro, and A. Vainshtein -- Ramified coverings of \(S^2\) with one degenerate branching point and enumeration of edge-ordered graphs
  • S. Tabachnikov -- On zeros of the Schwarzian derivative
  • V. A. Vassiliev -- Stratified Picard-Lefschetz theory with twisted coefficients
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