SCIENTIFIC PROGRAM ACTIVITY

October  1, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

January 10-12, 2014
Conference on Hamiltonian PDEs: Analysis, Computations and Applications
Fields Institute, Toronto
In honour of Walter Craig on the occasion of his 60th birthday

Organizing Committee
Philippe Guyenne, University of Delaware
David Nicholls, University of Illinois at Chicago
Catherine Sulem, University of Toronto

Registration on site Jan. 9
Fees: $50, (waived for invited speakers)
Fees cover meeting materials and refreshments, Conference banquet January 11, tickets $75)
Schedule Abstracts Toronto Hotels and Housing

Overview

Partial Differential Equations (PDEs) are a fundamental tool in the modeling of phenomena found in the physical, biological and social sciences, and science as a whole has advanced exponentially as our understanding of PDEs has increased over the centuries. PDEs with Hamiltonian structure are a distinguished subset of these which not only model systems with conserved quantities (e.g., energy and momentum), but also possess an array of special techniques for their analysis.
Applications of these arise in fluid mechanics, plasma physics, and nonlinear optics, and major advances are still being made regarding their rigorous analysis and numerical simulation. One unifying theme of this conference will be the interaction of specialists in dynamical systems, Kolmogorov-Arnold-Moser (KAM) and Nash-Moser theory, normal form theory, variational methods, harmonic analysis and the classical techniques of PDE theory, as well as applied and numerical analysts, and experts in ocean waves.
The field is extremely broad and has attracted a wide range of researchers. This conference will be an opportunity to bring together a group of world-class experts in the field of Hamiltonian PDEs where Walter Craig has had a great influence, to present and discuss the latest developments in this fast-moving, applications-oriented field.

In honour of Walter Craig on the occasion of his 60th birthday

Invited Speakers

Dario Bambusi (Universita di Milano)
Claude Bardos (Universite Paris 7)
Massimiliano Berti (Universita di Napoli)
Jerry Bona (UIC)
Robert Brandenberger (McGill University)
Constantine Dafermos (Brown University)
Bernard Deconinck (University of Washington)
Nicky Kamran (McGill University)
Sergei Kuksin (Universite Paris 7)
David Lannes (ENS, Paris)
Rafael de la Llave (Georgia Tech)
David Nicholls (University of Illinois at Chicago)
Jean-Claude Saut (Universite Paris Orsay)
Harvey Segur (University of Colorado)
Peter Sternberg (Indiana University)
Konstantina Trivisa (University of Maryland)
Gene Wayne (Boston University)

Vladimir Zakharov (University of Arizona)

Schedule
Friday Jan 10, 2014

8:45

Breakfast and welcome

9:00 - 9:40

S. Kuksin
Weakly non-linear completely resonant hamiltonian PDEs and the problem of weak turbulence

9:45 -10:25

D. Lannes
Water waves with vorticity and asymptotics

10:30 - 11:00

Coffee break

11:00 - 11:40 K. Trivisa
On a nonlinear model for tumor growth: Global in time weak solutions
11:45 - 12:25 V. Zakharov
Hasselmann equation revisited
12:30 - 2:00 lunch
2:00 - 2:40 P. Sternberg
Kinematic vortices in a thin film driven by an applied current
2:45 - 3:25 J.-C. Saut
Dispersive perturbations of Burgers and hyperbolic equations
3:30 - 4:00 Coffee break
4:00 - 4:40 M. Berti
KAM for quasi-linear KdV
4:40- 5:00 O. Trichtchenko
Stability of near-resonant gravity-capillary waves

Saturday, Jan 11, 2014

9:00 - 9:40 R. Brandenburger
Partial Differential Equations with Random Coefficients in Inflationary Cosmology
9: 45 - 10: 25

C. Bardos
The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in Fluid Mechanics and Semi-classical Limits

10: 30 - 11:00 Coffee break
11:00 - 11: 40 R. de la Llave
11:45- 12:25 N. Kamran
A Singular initial-boundary value problem for non-linear wave equations and holography in asymptotically anti-de Sitter manifolds
12: 30 - 2:00 Lunch
2:00 - 2:40 C. Dafermos
Long-time behavior of periodic solutions to scalar conservations laws in several space dimensions
2:45 - 3:25 D. Nicholls
Layered Media Scattering: Fokas Integral Equations and Boundary Perturbation Methods
3:30 - 4:00 Coffee break
4:00 - 4:40 H. Segur
Three-wave resonant interactions Part 1
4:40 - 5:00 R. Martin
Three-wave resonant interactions Part 2
5:00 - 5:20 C. Fazioli
Overlapping Patches for Dynamic Problems
7:00 pm

Dinner, tickets $75, on sale Jan. 10

Sunday Jan 12, 2014

9:30 - 10:10 G. Wayne
Justification of the nonlinear Schödinger equation for two-dimensional gravity driven water waves
10:15 - 10:55 J. Bona
Long-crested wave propagation
11:00 - 11:30 Coffee break
11:30 - 12:10 B. Deconinck
High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
12:15 - 12:55 D. Bambusi
An averaging theorem for FPU in the thermodynamic limit

 

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