Dr. Catherine Sulem

University of Toronto

Dr. Sulem received the degree Docteur ès Sciences in 1983 from the Université Paris-Nord. In France, she held positions with the CNRS at the University of Nice and the École Normale Supérieure in Paris. Since 1990, Dr. Sulem has been a professor in the Department of Mathematics at the University of Toronto. Over the course of her career, Dr. Sulem has served as an editor of several journals, including the Canadian Journal of Mathematics, Proceedings of the AMS, SIAM Journal of Mathematical Analysis, Mathematische Zeitschrift and Annales Mathématiques du Québec.

Dr. Sulem's research focuses on nonlinear dynamics in various fields of physics, in particular, evolution equations that describe wave phenomena in fluids, nonlinear optics and plasma physics. She has significantly contributed to these fields, notably co-authoring with Pierre-Louis Sulem a monograph dedicated to the Nonlinear Schrödinger equation, a work that has been a source of inspiration for numerous mathematicians. Together with Vladimir Zakharov and Walter Craig, Dr. Sulem is credited with a formulation of the water-wave equations which is pivotal to current research in mathematical analysis, numerical simulations and in the derivation of asymptotic models.

These results only scratch the surface of Dr. Sulem's extensive work. She has authored or co-authored over 100 publications, leaving a profound impact on various domains of physics and mathematics.

In addition to her research endeavors, Dr. Sulem actively contributes to the cultivation and advancement of future mathematicians. She has played a pivotal role in mentoring numerous postdoctoral fellows and graduate students. Furthermore, her achievements are recognized through her fellowship in the Royal Society of Canada, the American Mathematical Society and the Canadian Mathematical Society. Dr. Sulem has been a featured speaker at many international conferences, including the 2019 ICIAM where she delivered the AWM-SIAM Sonia Kovalevsky Prize lecture.

Dr. Sulem’s productive and prolific career has left (and continues to leave) a profound impact on multiple domains of mathematics. The CMS is proud to award her the 2024 Jeffery-Williams Prize for her many influential contributions to both her research field(s) and the broader realm of mathematics.

Abstract

Monday, June 3: 13:30-14:30

ARTS 241 Lecture Hall

Effect of a variable bottom topography on surface water waves

We investigate the effect of the bottom topography on the evolution of surface waves. It is a problem of significance for ocean dynamics in coastal regions where waves are strongly affected by the topography. The literature on models of free surface water waves over a variable depth is extensive. In the presence of topography, there are several asymptotic scaling regimes of interest, including long-wave hypotheses for the evolution of the free surface, and short scale and/or long scale variations in the variable bottom. A central object in the analysis of the water wave problem is the Dirichlet-Neumann operator and our study concerns its spectrum in the context of the water wave system linearized near equilibrium in a domain with a variable bottom assumed to be a smooth periodic function. We use the analyticity of the Dirichlet-Neumann operator with respect to the bottom variation and combine it with general properties of elliptic systems and spectral theory for self-adjoint operators to develop a Bloch-Floquet theory and describe the structure of its spectrum. We find that, under some conditions on the bottom varia- tions, the spectrum is composed of bands separated by gaps which are zones of forbidden energies, and we give explicit formulas for their sizes and locations.