February 21, 2024

Fields Institute Colloquium/Seminar in Applied Mathematics

Organizing Committee:
Jim Colliander (U of Toronto)
Walter Craig (McMaster)
Catherine Sulem (U of Toronto)
Robert McCann (U of Toronto)
Adrian Nachman (U of Toronto)   
Mary Pugh (U of Toronto)  


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.

Upcoming Talks

Monday July 8
1:10 p.m.
Stewart Library

Ricardo Barros, IMPA (Instituto Nacional de Matematica Pura e Aplicada, Brazil)
Two-dimensional Nonlinear Internal Wave

Large amplitude internal solitary waves excited typically by the interaction of tidal currents with bottom topography have been observed frequently in coastal oceans through in-situ measurements and satellite images. Although there has been a considerably intensive research on nonlinear internal waves, most of the existing work is devoted strictly to the one-dimensional case. To study the evolution of two-dimensional large amplitude internal waves in a two-layer system with variable bottom topography, we derive a fully two-dimensional strongly nonlinear model. This is a generalization of the one-dimensional model of Choi, Barros & Jo (2009) that is known to be free from shear instability for a wide range of physical parameters. After investigating shear instability of the regularized model for flat bottom, weakly two-dimensional and weakly nonlinear limits are discussed.


Previous Talks
Wednesday Feb 27
3:10 p.m.
Stewart Library

Francois Hamel, Université d'Aix-Marseille
Reaction-diffusion equations and traveling fronts.

Traveling fronts are an important class of solutions of semilinear parabolic PDEs of the reaction-diffusion type. They usually describe the transition between two stationary states. In this talk, I will first review the standard notions of traveling fronts and some of the main existence and qualitative results. The traveling fronts can also be viewed as examples of generalized transition fronts. These new notions involve uniform limits with respect to some families of hypersurfaces. The existence of transition fronts has been proved recently in various contexts where the standard notions of fronts make no sense anymore. I will then focus on some uniqueness and further qualitative properties of the transition fronts, including the characterization of their global mean speed for some bistable equations. The talk will be based on some joint works with H. Berestycki and H. Matano.

Wednesday July 11
4:10 p.m.
Room 230
Darryl D. Holm, Imperial College London
Momentum Maps, Image Analysis & Solitons

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