Workshop

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: Random Walks and Singular Diffusions,Charles Newman Strange attractors in periodically forced systems undergoing Hopf bifurcations, Lai-Sang Young Invariant Measures for Nonlinear Partial Differential Equations, Bjorn Birnir Hamiltonian formalism for integrable systems and Riemann surfaces, Kirill Vaninsky Camassa-Holm Equation, Euler-Poincare and Geodesic Flows on the Diffeomorphism Group, Darryl Holm 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