Fields Colloquium/Seminar in Applied Math

The Fields Institute Colloquium/Seminar in Applied Mathematics is a  monthly colloquium series for mathematicians in the areas of applied  mathematics and analysis. The series alternates between colloquium  talks by internationally recognized experts in the field, and less formal,  more specialized seminars.In recent years, the series has featured  applications to diverse areas of science and technology; examples  include super-conductivity, nonlinear wave propagation, optical fiber  communications, and financial modeling. The intent of the series is to  bring together the applied mathematics community on a regular basis,  to present current results in the field, and to strengthen the potential for  communication and collaboration between researchers with common  interests. We meet for one session per month during the academic  year. The organizers welcome suggestions for speakers and topics. 

The Fields Institute also hosts a page about this Colloquium/Seminar series. 

More information can be found at the following link: http://www.fields.utoronto.ca/programs/scientific/09-10/applied_math/

Details

Two Existence Problems in Interfacial Fluid Dynamics

by David Ambrose  (www) | Drexel University
Time: 15:10  (Wednesday, Mar. 21, 2012)
Location: Fields Institute, 222 College St
Abstract:
Much progress has been made in recent years in existence theory for initial value problems in interfacial fluid dynamics. We will introduce two other existence problems: the problem of global weak solutions for interfacial flows with surface tension, and the problem of time-periodic interfacial flows. We will report on progress for these problems, which includes both analytical and numerical work. This is joint work with Milton Lopes Filho, Helena Nussenzveig Lopes, Walter Strauss, and Jon Wilkening.

Details

The Geometry of Light Transport

by Christian Lessig  (www) | Technische Universitaet Berlin and University of Toronto
Time: 14:10  (Wednesday, Mar. 21, 2012)
Location: Fields Institute, 222 College Street
Abstract:
Founded on Lambert's radiometry from the 18th century, light transport theory describes the propagation of visible light energy in macroscopic environments. While already in 1939 the theory was characterized as "a case of `arrested development'", no re-formulation has been undertaken since then. Following recent literature, we develop the geometric structure of light transport by studying the short wavelength limit of a lifted representation of electromagnetic theory on the cotangent bundle. This shows that light transport is a Hamiltonian system with the transport of the light energy density, the phase space representation of electromagnetic energy, described by the canonical Poisson bracket. A non-canonical Legendre transform relates light transport theory to geometric optics, and by considering measurements, as did Lambert, we are able to obtain classical concepts from radiometry. In idealized environments where the Hamiltonian vector field is defined globally, we show that light transport is a Lie-Poisson system for the group Diff_{can}(T^*Q) of canonical transformations. The Poisson bracket then describes the infinitesimal coadjoint action in the Eulerian representation while the momentum map yields the convective light energy density as Noetherian quantity. The group structure also unveils a tantalizing similarity between ideal light transport and the ideal Euler fluid, warranting to consider the systems as configuration and phase space analogues of each other.

Dates in this series

· Wednesday, Apr. 14, 2010: Denjoy-Schwartz and Hamilton-Jacobi (Albert Fathi)
· Wednesday, May. 26, 2010: New Theories of Imagery and Implications for Image Segmentation (Dr Garry Newsam)
· Wednesday, Jun. 02, 2010: Recovering the electrical conductivity from interior data (Prof. Alex Tamasan )
· Wednesday, Jul. 28, 2010: The classical capacity of a quantum channel (Chris King)
· Friday, Aug. 20, 2010: The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality (Apala Majumdar)
· Wednesday, Nov. 10, 2010: Optimal transport and geodesics for H1 metrics on diffeomorphism groups (Boris Khesin)
· Wednesday, Nov. 24, 2010: Discrete Elastic Rods and Viscous Threads (Eitan Grinspun)
· Thursday, Nov. 25, 2010: From Sorcery to Science: how Hollywood Physics impacts the Sciences (Eitan Grinspun)
· Wednesday, Dec. 08, 2010: Introduction to the renormalization group as a rigorous tool in probability theory (Abdelmalek Abdesselam)
· Wednesday, Mar. 16, 2011: Breakdown of Smoothness in the Muskat Problem (Charles Fefferman)
· Wednesday, Apr. 20, 2011: Mixed-mode solutions in the differentially heated rotating annulus (Greg Lewis)
· Wednesday, Apr. 20, 2011: Numerical simulation of Faraday waves (Nicolas Perinet)
· Wednesday, Jun. 01, 2011: Resonances and long time integration of nonlinear Schroedinger equations (Erwan Faou)
· Wednesday, Nov. 23, 2011: A self-dual polar decomposition for vector fields (Nassif Ghoussoub)
· Wednesday, Mar. 21, 2012: Two Existence Problems in Interfacial Fluid Dynamics (David Ambrose)
· Wednesday, Mar. 21, 2012: The Geometry of Light Transport (Christian Lessig)
· Thursday, Apr. 12, 2012: Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion (Evelyn Lunasin)
· Thursday, Apr. 12, 2012: 'Ultimate state'' of two-dimensional Rayleigh-B\'enard convection (Charles Doering)