SCIENTIFIC PROGRAM ACTIVITY

December 22, 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

Registration on-site Nov. 24
Fees $75,
waived for students & invited speakers.
(fees cover coffee breaks and meeting materials)
Reimbursement information for funded participants Confirmed Participants
Information for speakers Directions to Fields
Video of the talks Accommodation in Toronto
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 Dmitry Fuchs (UC Davis)
Cohomology of Lie algebra of Hamiltonian vector fields: experimental data, conjectures, and theorems (Slides)
10:15-10:45am Coffee Break
10:45-11:15am Yulij Ilyashenko (Cornell University/IUM)
Rotation numbers and moduli of elliptic curves
11:30-12:00pm J. Richard 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

Vadim Kaloshin (University of Maryland)
On Arnold diffusion for convex Hamiltonians (Slides)

2:45-3:15pm Yael Karshon (University of Toronto)
Lie groupoids for space robots (Slides)
3:15-3:45pm Coffee Break
3:45-4:15pm Oleg Bogoyavlenskij (Queen's University)
A family of solutions to the Arnold's problem on the non-degenerate integrability
4:30-5:00pm Konstantin Khanin (University of Toronto)
From linearization to rigidity theory
5:00-7:00pm Reception (cash bar)
Tuesday November 25, 2014.
9:00-9:30am Sergei Chmutov (Ohio State University)
Partial duality of hypermaps (Slides)
9:45-10:15am Victor Goryunov (University of Liverpool)
Local invariants of maps between 3-manifolds (Slides)
10:15-10:45am Coffee Break
10:45-11:15am Lisa Jeffrey (University of Toronto)
Kirwan surjectivity for hyperkähler manifolds (Slides)
11:30-12:00pm Keith Moffatt (University of Cambridge)
Relaxation under topological constraints and the breaking of these constraints
12:00-2:00pm Lunch Break
2:00-2:30pm Inna Scherbak (Tel-Aviv University)
Linear ODEs from an algebraic point of view (Slides)
2:45-3:15pm Gerard Misiolek (University of Notre Dame)
The Morse-Littauer theorem in hydrodynamics
3:15-3:45pm Coffee Break
3:45-4:15pm Vladimir Dragovic (University of Texas, Dallas)
Algebro-geometric approach to the Schlesinger equations and the Poncelet polygons (Slides)
4:30-5:00pm Walter Craig (Fields Institute/ McMaster University)
Vortex filament dynamics (Slides)
7:00-9:00pm

High-School Student Session Talks

Gabor Domokos (Budapest Univ. of Technology and Economics)
Story of the Gömböc
Dror Bar-Natan
(University of Toronto)
On Maps, Machines and Roaches

Wednesday November 26, 2014.
9:00-9:30am Pavel Etingof (MIT)
Poisson homology, D-modules on Poisson varieties, and complex singularities (Slides)
9:45-10:15am Gabor 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 Alexander Givental (UC Berkeley)
Oscillating integrals in the mirror K-theory
11:30-12:00pm Sabir Gusein-Zade (Moscow State University)
Some duality properties of invertible polynomials
12:00-2:00pm Lunch Break
2:00-2:45pm Dror Bar-Natan (University of Toronto)
Dessert: Hilbert's 13th Problem, in full color
2:45-4:00pm Coffee Break
4:00pm
Math Colloquium: Lawrence Craig Evans (UC Berkeley)
Convexity, nonlinear PDE and principal / agent problems
Location:
BA6183, Bahen Center, 40 St. George St
.
Thursday November 27, 2014.
9:00-10:00am Michael Shapiro (Michigan State University) and Alexander Vainshtein (University of Haifa)
Cluster algebras and integrable systems
10:00-10:45am Coffee Break
10:45-11:15am Michael Polyak (Technion)
From 3-manifolds to planar graphs and cycle-rooted trees (Slides)
11:30-12:00pm Sergei Lando (University HSE, Moscow)
On graph invariants related to finite order knot invariants
12:00-2:00pm Lunch Break
2:00-2:30pm Emmanuel Ferrand (Université de Paris 6)
Remarks and questions about apparent contours, envelopes and generating families
2:45-3:15pm Victor Ginzburg (UC Santa Cruz)
The motion of a charge in a magnetic field
3:15-3:45pm Coffee Break
3:45-4:15pm Anatoly Vershik (Steklov Institute of Math., St. Petersburg)
Dynamics of metrics and scaling entropy of the group action (Slides)
4:30-5:00pm Oleg Viro (Stony Brook University)
Head to tail compositions (Slides)
7:00-9:00pm Open Problem Session
Friday November 28, 2014.
9:00-9:30am Vladlen Timorin (University HSE, Moscow)
On maps taking lines to plane curves (Slides)
9:45-10:15am Dror Bar-Natan (University of Toronto)
Finite type invariants of doodles
10:15-10:45am Coffee Break
10:45-11:15am Yakov Eliashberg (Stanford University)
Construction and classification of contact structures
11:30-12:00pm Alexander Shnirelman (Concordia University)
Shooting problem for the 2-d ideal incompressible fluid
12:00-2:00pm Lunch Break
2:00-2:45pm Andrei Gabrielov (Purdue University)
Classification of spherical quadrilaterals (Slides)
2:45-3:15pm Vladimir Vladimirov (University of York, UK)
Arnold stability of time-oscillating flows (Slides)
3:15-3:45pm Coffee Break
3:45-4:15pm Anton Zorich (Université de Paris 7)
Lyapunov exponents of the Hodge bundle and diffusion in periodic billiards(Slides)
4:30-5:00pm Maxim Kazarian (Steklov Institute of Math, Moscow)
On Salmon's enumeration of tangential singularities

 

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