## 2020 CRM-Fields-PIMS Prize Lectures: Catherine Sulem

- Start Date: 11/24/2020
- End Date: 11/25/2020

Online

Catherine Sulem, F.R.S.C. and Professor of Mathematics at the University of Toronto, has been awarded the CRM-Fields-PIMS prize for outstanding achievement in the mathematical sciences. Professor Sulem is the second woman to be awarded the prize since its inception in 1994.

“It is a great honour for me to be awarded the 2020 CRM-Fields-PIMS prize,” said Professor Sulem, upon being notified of her award. “I have participated in many wonderful programs at the Institutes and would like to thank them for their support of the entire Canadian mathematical community. I am also grateful to my collaborators, who have played a vital role in my research. I thank all of them for their inspiration and friendship.”

Professor Sulem is being recognized for her numerous and influential contributions to the study of non-linear partial differential equations. Her deep results on the non-linear Schrödinger equation resolved multiple questions that had resisted analysis for years. In particular, her work is central to the understanding of self-focusing singularities to this equation. Her analysis of water waves introduced powerful new probabilistic ideas to that field. These and other ground-breaking achievements have been acknowledged earlier through her election as a Fellow of both the Royal Society of Canada and the American Mathematical Society, through winning the Krieger-Nelson prize of the Canadian Mathematical Society and the 2019 Association for Women in Mathematics - Society for Industrial and Applied Mathematics (AWM-SIAM) Sonia Kovalevsky Lecture, and through the award of a Killam Research Fellowship of the Canada Council for the Arts.

The CRM-Fields-PIMS prize is the premier Canadian award for research achievements in the mathematical sciences. It is awarded jointly by the three Canadian mathematics institutes: Centre de Recherches Mathématiques in Montreal, the Fields Institute in Toronto, and the Pacific Institute for the Mathematical Sciences in Vancouver. Professor Sulem will receive a monetary award and an invitation to present a lecture at each institute.

The prize was established by the Centre de Recherches Mathématiques and the Fields Institute as the CRM-Fields prize in 1994, and the Pacific Institute for the Mathematical Sciences became an equal partner in 2005.

Tuesday, November 24th

**The dynamics of ocean waves**

Many aspects of mathematical analysis were originally motivated by the study of fluid dynamics; in particular, waves and currents in bodies of water. I will discuss how mathematical analysis combined with asymptotic theory and accurate numerical simulations contributes, in turn, to a better understanding of the dynamics of ocean waves both at the surface of the ocean and in its interior, in regular situations and in extreme events.

Wednesday, November 25th

**The Derivative Nonlinear Schrödinger Equation: Global Existence and Soliton Resolution
**

The Derivative Nonlinear Schrödinger equation arises as a long-wave, small amplitude model in the context of Magnetohydrodynamics for conducting fluids, when the Hall effect is taken into account in the Ohm’s law. A central property of this equation, discovered by Kaup and Newell in 1978, is that it is an integrable system, solvable through the inverse scattering method. I will show how inverse scattering may provide tools to address fundamental questions such as global existence and long-time behaviour of solutions for large data, asymptotic stability of solitons, and, more generally, the soliton resolution conjecture which refers to the property that, for large times, solutions decompose into a finite number of well-separated solitons, and a small dispersive part.

Please register here.