SCIENTIFIC PROGRAM ACTIVITY

November 21, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES


November 24-28, 2014
Conference
Legacy of Vladimir Arnold
at
Fields Institute, 222 College St., Toronto

Local Organization Committee
M. Boyko, I. Gorbovickis, L. Kadets,
B. Khesin, A. Khovanskii, J. Mracek,
S. Tabachnikov, V.Vladimirov

Scientific Committee
E. Bierstone (Toronto), H. Hofer (IAS), B. Khesin (Toronto), A. Khovanskii (Toronto), S.Tabachnikov (Penn State and ICERM), A. Varchenko (North Carolina)

OVERVIEW

Vladimir Igorevich Arnold, 1937–2010, was one of the greatest mathematicians of the 20th century. He has made fundamental contributions to numerous fields of mathematics, including dynamical systems, classical mechanics, singularity theory, algebraic geometry, topology and catastrophe theory. In 1957, at the age of 19, Arnold, together with his teacher A. N. Kolmogorov, solved Hilbert’s 13th problem on representation of continuous functions. The results contained in his doctoral thesis “Small denominators and stability problems in classical and celestial mechanics” became one of the cornerstones of the famous KAM theory, named after its creators Kolmogorov, Arnold, and Moser. Arnold's monographs “Mathematical Methods of Classical Mechanics” and “Ordinary Differential Equations” became classical university textbooks.

The conference "Legacy of Vladimir Arnold" to be held at the Fields Institute will celebrate the work and life of this distinguished mathematician and remarkable human being. In addition to research talks, it will host an evening session for high school students on Tuesday, November 25 and an evening round table devoted to open problems on Thursday, November 27.

Arnold's 60th anniversary conference, ArnoldFest, was held at the Fields Institute in 1997.

Proceeding of the conference will be published in the "Arnold mathematical journal", a recently established journal based in the Stony Brook University, covering a broad range of mathematical domains. Deadline for submission: November 28, 2014.

Speaker Abstracts


Monday November 24, 2014.
9:00-9:30am On-Site Registration
9:35-9:45am Introduction
9:45-10:15am D. Fuchs (UC Davis)
Cohomology of Lie algebra of Hamiltonian vector fields: experimental data, conjectures, and theorems
10:15-10:45am Coffee Break
10:45-11:15am Yu. Ilyashenko (Cornell University/IUM)
Rotation numbers and moduli of elliptic curves
11:30-12:00pm J.R. Bond (CITA, University of Toronto) and S. Shandarin (University of Kansas)
Zeldovich-Arnold's theory of the cosmic web
12:00-2:00pm Lunch Break
2:00-2:30pm

V. Kaloshin (University of Maryland)
On Arnold diffusion for convex Hamiltonians

2:45-3:15pm Y. Karshon (University of Toronto)
Lie groupoids for space robots
3:15-3:45pm Coffee Break
3:45-4:15pm O. Bogoyavlenskij (Queen's University)
A family of solutions to the Arnold's problem on the non-degenerate integrability
4:30-5:00pm K. Khanin (University of Toronto)
From linearization to rigidity theory
5:00-7:00pm Reception (cash bar)
Tuesday November 25, 2014.
9:00-9:30am S. Chmutov (Ohio State University)
Partial duality of hypermaps
9:45-10:15am V. Goryunov (University of Liverpool)
Local invariants of maps between 3-manifolds
10:15-10:45am Coffee Break
10:45-11:15am L. Jeffrey (University of Toronto)
Kirwan surjectivity for hyperkähler manifolds
11:30-12:00pm K. Moffatt (University of Cambridge)
Relaxation under topological constraints and the breaking of these constraints
12:00-2:00pm Lunch Break
2:00-2:30pm I. Scherbak (Tel-Aviv University)
Linear ODEs from an algebraic point of view
2:45-3:15pm G. Misiolek (University of Notre Dame)
The Morse-Littauer theorem in hydrodynamics
3:15-3:45pm Coffee Break
3:45-4:15pm V. Dragovic (University of Texas, Dallas)
Algebro-geometric approach to the Schlesinger equations and the Poncelet polygons
4:30-5:00pm W. Craig (Fields Institute/ McMaster University)
Vortex filament dynamics
7:00-9:00pm G. Domokos (Budapest Univ. of Technology and Economics),
D. Bar-Natan
(University of Toronto)
High-School Student Session Talks
Wednesday November 26, 2014.
9:00-9:30am P. Etingof (MIT)
Poisson homology, D-modules on Poisson varieties, and complex singularities
9:45-10:15am G. Domokos (Budapest Univ. of Technology and Economics)
The Gömböc and the evolution of pebble shapes
10:15-10:45am Coffee Break
10:45-11:15am A. Givental (UC Berkeley)
Oscillating integrals in the mirror K-theory
11:30-12:00pm S. Gusein-Zade (Moscow State University)
Some duality properties of invertible polynomials
12:00-2:00pm Lunch Break
2:00-2:45pm D. Bar-Natan (University of Toronto)
Dessert: Hilbert's 13th Problem, in full color
2:45-4:00pm Coffee Break
4:00pm Math Colloquium: C. Evans (UC Berkeley)
Convexity, nonlinear PDE and principal / agent problems
Thursday November 27, 2014.
9:00-10:00am M. Shapiro (Michigan State University) and A. Vainshtein (University of Haifa)
Cluster algebras and integrable systems
10:00-10:45am Coffee Break
10:45-11:15am M. Polyak (Technion)
From 3-manifolds to planar graphs and cycle-rooted trees
11:30-12:00pm S. Lando (University HSE, Moscow)
On graph invariants related to finite order knot invariants
12:00-2:00pm Lunch Break
2:00-2:30pm E. Ferrand (Université de Paris 6)
Remarks and questions about apparent contours, envelopes and generating families
2:45-3:15pm V. Ginzburg (UC Santa Cruz)
The motion of a charge in a magnetic field
3:15-3:45pm Coffee Break
3:45-4:15pm A. Vershik (Steklov Institute of Math., St. Petersburg)
Dynamics of metrics and scaling entropy of the group action
4:30-5:00pm O. Viro (Stony Brook University)
Head to tail compositions
7:00-9:00pm Open Problem Session
Friday November 28, 2014.
9:00-9:30am V. Timorin (University HSE, Moscow)
On maps taking lines to plane curves
9:45-10:15am D. Bar-Natan (University of Toronto)
Finite type invariants of doodles
10:15-10:45am Coffee Break
10:45-11:15am Ya. Eliashberg (Stanford University)
Construction and classification of contact structures
11:30-12:00pm A. Shnirelman (Concordia University)
Shooting problem for the 2-d ideal incompressible fluid
12:00-2:00pm Lunch Break
2:00-2:45pm A. Gabrielov (Purdue University)
Classification of spherical quadrilaterals
2:45-3:15pm V. Vladimirov (University of York, UK)
Arnold stability of time-oscillating flows
3:15-3:45pm Coffee Break
3:45-4:15pm A. Zorich (Université de Paris 7)
Lyapunov exponents of the Hodge bundle and diffusion in periodic billiards
4:30-5:00pm M. Kazarian (Steklov Institute of Math, Moscow)
TBA

 

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