What is your research field?
My research field is originally partial differential equations and calculus of variations. I have been particularly interested in the mathematical analysis of the Ginzburg-Landau model of superconductivity and in vortex patterns observed in superconductivity and superfluids, as well as in their evolution. That led me to take a broader interest in particle systems that interact in a Coulombian way, which may be found from physics to approximation theory. Adding possible thermal effects raises questions which appear in random matrices or in certain models of theoretical physics, which led me to statistical mechanics and to the interface between analysis and probabilities.
What do you like about your job?
The intellectual stimulation, and the fact that the job does not repeat itself. One is always pushed to go a little further, to improve and renew oneself, to learn new things and explore new territories. I also like having exchanges with my colleagues, meeting younger ones (students, PhD students, postdocs), having the feeling I’m passing on the torch, and I very much appreciate the international aspect of the job, travelling often, forging connections with colleagues from various countries. And then of course there's the freedom, the freedom of working on what you want, with whom you want, at whatever time you want! All that is very valuable, let us not forget it.
Given your background, what does it mean for you to be an invited speaker at ICIAM?
It is true that I certainly represent (with some others) the most theoretical side of applied mathematics at this conference. The boundaries are in any case not so sharp and I enjoy pointing out that what I do is considered in France as part of applied mathematics (Section 26) whereas in the United States it undoubtedly falls under pure mathematics, the determining criterion being whether or not one demonstrates theorems. Let us rather think of 18th century mathematicians such as Fourier, D’Alembert or Lagrange, who above all sought to understand nature and invented for this very reason quite fundamental mathematical notions.
I personally like problems originating in physics (I have been working on problems coming from superconductivity and even from material science), which have de facto an external motivation: I like understanding them by looking for fundamental structures and methods while at the very same time producing results which have as concrete a physical meaning as possible. But in the end, a good part of mathematics, even mathematics which are considered as very “pure”, is also inspired by physics or by questions outside mathematics. Conversely, many questions in applied mathematics lead to “fundamental” mathematical questions. This very to-and-fro movement seems quite rich to me.
When I spoke at the "Foundations of Computational Mathematics" conference two years ago, it occurred to me for example that my concerns found an echo in those of that community. I hope it will be the case at ICIAM too, I am honored to be invited by this community. I have a great deal of admiration for my colleagues of applied mathematics who can actually solve practical questions and yield useful codes, which I would just be incapable of doing. I also think that the questions of contemporary science such as big data may also nurture very interesting questions in fundamental mathematics. Finally, I would like to take up the joke ‘There is not pure mathematics and applied mathematics, there is just good and bad mathematics’.
Sylvia Serfaty is a Silver Professor at Courant Institute of Mathematical Sciences, New York University.
More info about ICIAM2019