A Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences (NYU), Sylvia Serfaty was invited as a plenary speaker at the 2018 International Congress of Mathematicians in Rio de Janeiro. She answered our questions.
What are your research interests?
My research interests originally were PDEs and calculus of variations. I then particularly focused on the mathematical analysis of the Ginzburg-Landau model of superconductivity, and on vortex patterns that may be observed in superconductivity and superfluids, and on their evolution. It led me to work more generally on particle systems which interact in a Coulombian way, that are to be found from physics to approximation theory. Adding possible thermic effects raises questions which appear in random matrix or in certain models of theoretical physics, which brought me to statistical mechanics and to the interface between analysis and probabilities.
What brought you to do mathematics?
I had the intuition that I wanted to do research in mathematics when I was in highschool. We had exercices to solve at home and one of them gave me a rough time. I had spent some time on it and, in order to answer the question, I had finally demonstrated something more general than was asked. I had found out some sort of functional inequality (I don't remember precisely what). I had been erring and going around in circles and groping about, and in the end, I had found a solution. But above all, I had had a great time! I had been totally engrossed in it. It somehow was my first experience as a researcher... I remember presenting my solution at maths class: everyone was surprised, even the teacher. It gave me the hint. As I was wondering what could be my vocation, all of a sudden it appeared to me that research, which looked rather appealing (although I then had no precise idea of what it really was, just an intuition), met with a concrete research domain: mathematics, which seemed to match my brains - a taste for certainty, the pleasure of toying with a question... I then strived to fulfil the conditions to carry out this project of becoming a mathematician. I had no idea if I was capable of being one, but the first step was to study in a "classe préparatoire". That's where I had the chance to have Stéphane Hoguet as a teacher, and I pay tribute to his memory. He played an important role as he made me truly discover the beauty of mathematics and was the first one to believe in my capacity as a mathematician and to encourage me on that path.
What is it that you like as a mathematician?
I like being intellectually stimulated, and I like the fact that nothing repeats itself. You're always goaded to go a little further, to improve and refresh yourself, 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 you're passing on the torch, and I very much enjoy the international part of the job, travelling a lot, creating links with colleagues in 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 precious, let us not forget it.
Do you already know what you're going to talk about in Rio?... What does it mean to you, to participe in this congress?
Surely I know! From the moment I was invited, I've kept thinking about it, trying to imaging what my talk should look like, and the idea of it is maturing in my head, like elements of a jigsaw puzzle which fall into place. I'm going to speak about Coulomb systems, it will be my guiding thread, starting with the different problems which lead there, and ending with the techniques which have been developped, the available results and the open questions. There is a very delicate issue in terms of presentation: how shall I hint at the most possible themes to catch the largest possible audience, account for my work but also on others and on a whole research domain, yet giving enough details to give it flesh and body, not losing too many people, and all this in just one hour! As a matter of fact, we received yesterday a requirement specification from the organizers... This invitation is a great honour, but also a great responsability and a challenge to take up.
Sylvia Serfaty a Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University.