This workshop is to be held at the International House on the UC Berkeley campus, at 2299 Piedmont Avenue. On site registration for the workshop will be at the International House.

The core theme of this workshop is that of the probabilistic approach to the study of partial differential equations, following ideas and work of Henry McKean over five decades, as it has evolved and is sustained in contemporary research. Emphasis will be on six main themes which will be interlaced throughout the program, reflecting the central unity of the approaches to the underlying problems. In this way, researchers whose work is concentrated in one or another of these areas will be exposed to the main threads of the other areas. For each theme we have identified a main speaker who will provide an initial overview. There are six additional themes which are to be touched upon at this workshop.

The six main areas and their main speakers are:

1. Random Walks and Singular Diffusions,Charles Newman


2. Strange attractors in periodically forced systems undergoing Hopf bifurcations, Lai-Sang Young


3. Invariant Measures for Nonlinear Partial Differential Equations, Bjorn Birnir


4. Hamiltonian formalism for integrable systems and Riemann surfaces, Kirill Vaninsky


5. Camassa-Holm Equation, Euler-Poincare and Geodesic Flows on the Diffeomorphism Group, Darryl Holm


6. Random Navier-Stokes Systems, Jonathan Mattingly

Schedule

Monday, December 5 (Sproul Rooms)
9:15 Welcome
9:30 –10:30 Peter D Lax: An abstraction of Saint Venant's Principle
Break
11:00-12:00 Harry Dym: Inverse problems for canonical systems of differential equations
Lunch
1:30-2:30 F. Alberto Grünbaum: From X-ray tomography to noncommutative algebras of differential
operators
2:30-3:30 Jonathan C. Mattingly: Degenerately forced stochastic fluid equations and simple models with
anomalous dissipation
Break
4:00-5:00 Charles Newman: Scaling limit of two-dimensional critical percolation
5:00 Second Chances


Tuesday, December 6 (Sproul Rooms)
9:30 –10:30 Serguei Novikov: Topological Charge of The Sine-Gordon Solutions
Break
11:00-12:00 Paul Georges Malliavin: Stochastic differential geometry on the group of diffeomorphisms of
the circle
Lunch
1:30-2:30 Pierre Van Moerbeke: From random matrices to stochastic processes, via integrable systems
2:30-3:30 S. R. S. Varadhan: Homogenization of random Hamilton-Jacobi-Bellman equations
Break
4:00 Second Chances


Wednesday, December 7 (Home Room)
9:30 –10:30 Kirill Vaninsky: Hamiltonian formalism for integrable systems and Riemann surfaces
Break
11:00-12:00 Lai-Sang Young: Strange attractors in evolutionary PDEs
Lunch
1:30-2:30 David Cai: A Kinetic Theory for Fluctuation Dominated Neuronal Networks
2:30-2:45 Nicolas Ercolani: Loop Equations for the large N limit of Hermitean Random Matrices
2:45-3:00 Harvey Segur: Waves in shallow water
3:00-3:15 Brian Rider: Noise limits for complex eigenvalue


3:30 –5:00 Poster Session (Sproul Rooms)

Mark Alber: The Complex Geometry of Weak Piecewise Smooth Solutions of a Class of Integrable
Nonlinear PDE's
Enrique Loubet: Integration of Individual Flows of the Camassa-Holm Hierarchy and Genesis of
Solitons
Victor Moll: Landen transformations
Mina Ossiander: Stochastic Representations and the Navier-Stokes Equation
Emma Previato: Genus Two Isomonodromy Garnier System as a Higher Order Painleve VI Equation


Thursday, December 8 (Sproul Rooms)
9:30–10:30 Björn Birnir: Turbulent Flow of a Uniform Stream
Break
11:00-12:00 Craig Tracy: The Airy and Pearcey Processes
Lunch
1:30-2:30 Daniel Stroock: Some queer diffusions
2:30-3:30 Emma Previato: Commuting Partial Differential Operators
Break
4:00-5:00 Igor Krichever: Integrable linear equations and Riemann-Schottky type problems
5:00 Second Chances


Friday, December 9 (Home Room)
9:30–10:30 Anne Boutet de Monvel: NLS on the half-line: a Riemann-Hilbert approach for the case of
time-periodic boundary data
Break
11:00-12:00 Nirenberg, Louis: A geometric problem and the Hopf Lemma
Lunch
1:30-2:30 Mark A . Pinsky: Pointwise Fourier inversion in analysis and geometry
2:30-3:30 Jalal Shatah: TBA
Break
4:00 Henry McKean: Why the Gauss distribution is a prime

Funding

Important