The Arnoldfest: Proceedings of a Conference in Honour of V.I. Arnold for His Sixtieth Birthday(Fields Institute Communications)

This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over - including several from 'Arnold's school' - gave illuminating talks and lively poster sessions. The presentations focussed on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program.The topics of the lectures are: From Hilbert's Superposition Problem to Dynamical Systems; Symplectization, Complexification, and Mathematical Trinities; and, Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's 'Recollections', concerning some of the history of KAM theory.

Table of Contents:
From Hilbert's superposition problem to dynamical systems by V. I. Arnold Recollections by J. Moser Symplectization, complexification and mathematical trinities by V. I. Arnold Topological problems in wave propagation theory and topological economy principle in algebraic geometry by V. I. Arnold Geometry and control of three-wave interactions by M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins Standard basis along a Samuel stratum, and implicit differentiation by E. Bierstone and P. D. Milman A global weighted version of Bezout's theorem by J. Damon Real Enriques surfaces without real points and Enriques-Einstein-Hitchin 4-manifolds by A. Degtyarev and V. Kharlamov On the index of a vector field at an isolated singularity by W. Ebeling and S. M. Gusein-Zade The exponential map on $\mathcal{D}^s_\mu$ by D. G. Ebin and G. Misiolek Zeldovich's neutron star and the prediction of magnetic froth by M. H. Freedman Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds by K. Fukaya and K. Ono Multiplicity of a zero of an analytic function on a trajectory of a vector field by A. Gabrielov Singularity theory and symplectic topology by A. B. Givental On enumeration of meromorphic functions on the line by V. V. Goryunov and S. K. Lando Pseudoholomorphic curves and dynamics by H. Hofer and E. Zehnder Bifurcation of planar and spatial polycycles: Arnold's program and its development by Yu. S. Ilyashenko and V. Yu. Kaloshin Singularity which has no $M$-smoothing by V. M. Kharlamov, S. Yu. Orevkov, and E. I. Shustin Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces by B. Khesin and A. Rosly Newton polyhedra, a new formula for mixed volume, product of roots of a system of equations by A. Khovanskii Interactions of Andronov-Hopf and Bogdanov-Takens bifurcations by W. F. Langford and K. Zhan Solutions of the qKZB equation in tensor products of finite dimensional modules over the elliptic quantum group $E_{\tau,\eta}sl_2$ by E. Mukhin and A. Varchenko Schrodinger operators on graphs and symplectic geometry by S. P. Novikov On the dominant Fourier modes in the series associated with separatrix splitting for an a-priori stable, three degree-of-freedom Hamiltonian system by M. Rudnev and S. Wiggins Homology of $i$-connected graphs and invariants of knots, plane arrangements, etc. by V. A. Vassiliev On Arnold's variational principles in fluid mechanics by V. A. Vladimirov and K. I. Ilin On functions and curves defined by ordinary differential equations by S. Yakovenko Global finiteness properties of analytic families and algebra of their Taylor coefficients by Y. Yomdin.