Maryna Vyazovska

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Confédération Helvétique

Maryna Vyazovska earned a doctorate in Bonn in 2013 and has been a post-doctoral researcher at the Berlin Mathematical School and the Humboldt University of Berlin. She has been Minerva Distinguished Visitor in Princeton and currently holds a tenure-track assistant professorship at the École Polytechnique Fédérale de Lausanne. Maryna received the Clay Research Award and the SASTRA Ramanujan Prize for her work on sphere packing and modular forms, and the 2018 New Horizons Prize in Mathematics.

How would you explain your research to a non-specialist? 

How I explain my research depends on the person I am talking to. Someone who is not a specialist in mathematics is a probably a specialist in something else and it’s always easier to explain something when you know what the person is interested in.

My experience is that people remember very little from the mathematics they learnt at school and talking about mathematics it’s usually not a very good way to connect with people. This is on the other hand different when it comes to scientists working in some other sciences: many of my friends work for example as programmers. People that work in IT don’t do academic mathematics, but they do know quite a lot, so it’s easy to explain to them. 

Let’s explain your research to the readers of the EWM newsletter:

I think of myself as a number theorist, meaning that the problems I work on are usually problems in number theory. More specifically, my area of specialisation is automorphic forms. What I try to do is not developing the theory of automorphic forms itself but rather searching for interesting applications. These include the theory of elliptic curves, and through elliptic curves, there is a connection to diophantine equations and to rationality results.

Another direction in which I work is the connections between automorphic forms and Fourier analysis.

You recently received the  Clay Research Award: can you tell us something about the sphere-packing problems and about your results?

The name “sphere-packing” kind of speaks for itself: this is the problem of packing equally sized d-dimensional balls into the d-dimensional Euclidean space and it is one of the classical geometric problems. It turns out that in dimensions 8 and 24 this problem has a particularly nice solution and this solution is not geometric or combinatorial but it comes from harmonic analysis on the Euclidean space. This is the reason why I became interested in this problem and then I found this solution.

Can you tell us something about your story? When have you decided to be a mathematician and why?

My path was quite smooth. In Kiev, I attended a school where there was a special curriculum in the natural sciences and I was involved in mathematics olympiads and similar activities. When the time came to decide at which university I wanted to study it was quite natural to me to study mathematics. I got a Bachelor degree in Kiev and by the end of my bachelor I realised that I was not so much interested in the mathematical competitions anymore, but I realised that mathematical research was also very interesting.

For my master degree I moved to Germany, Kaiserslautern, and then I obtained my PhD in Bonn. One more thing, related to why I decided to become a mathematician I remember that when I was a high school student I read a science fiction book, where the main character was a mathematician who had found new ways of solving differential equations. The most intriguing part was the beginning: a mathematician is giving a lecture at the university, some students come, some colleagues show up and everything is as usual. After the lecture, a strange person comes to talk to him. It turns out this person is a robot sent to Earth by some superior civilisation, with the job of taking care of whatever happens there.  Unfortunately, he is not doing its job very well. He is a kind robot who is trying to do its best, but he cannot predict the consequence of his decisions. He can control many things but he cannot predict the long-term consequences. The mathematician, on the other hand, has discovered a way to predict the behaviour of solutions of chaotic differential equations. This was the most interesting part of the book and what I still remember about it. It made me think that being a mathematician was not a bad idea: imagine if you could compute and predict the consequences of our actions, it would be great. Of course from a mathematical point of view, it is way too naïve, and you don't expect to have mathematical tools like this,  but still, the whole story was very fascinating.

Do you have a dream? Any particular problem you dream to solve now?

My mathematical dream would be to solve a problem that nobody has thought of. You know how they say: good mathematicians can hit the goal that everybody sees, it’s the genius can hit the goal that nobody can see.

This is exactly what I find most inspiring in the history of mathematics: not when somebody solves a long-standing conjecture, but when somebody discovers a completely new direction or completely new phenomena that nobody had ever thought about before.

Think of when Grothendieck re-discovered algebraic geometry and put it in a completely new setting, or think of the discovery of fractals: in the mathematics that existed before there was simply no space for objects like these. Discoveries like these really change mathematics and the way we think about mathematics itself.

Do you have any other passions apart from Mathematics?

I have an 8-year-old son and he is a big part of my life. So I spend my time between mathematics and my family.

You will be one of the plenary speakers at the General Meeting of EWM next year: which is your point of view on issues about women in sciences and in particular in maths

Women are still somehow a minority in mathematics, and it doesn’t feel like the numbers are right. One reason for this I think is the prejudices that people have. The general mindset for parents is that boys are supposed to be good at science and girls are supposed to be good at something else. I find this attitude very harmful: when young adults choose a career for their future they don't really choose among all possibilities they have and don't find what they can do best.

It’s funny,  I hear young parents like me saying things like  "chess is very good for boys". Why? Chess is good for both boys and girls as long as they like it. iI your child is a boy it doesn’t imply he will be good at chess, and the opposite is also not true.

Another thing that certainly also plays a role is that the rules of the game for young scientists are not very family friendly. Many women that decide to leave the academic career do it when they have a family and realise they cannot be very mobile. The postdoctoral phase often requires people to move between countries. For someone who has a family, especially children, this is very difficult. I often think that a family friendly politics would benefit not only women but also men who are in academia and young people who want to pursue a scientific career.

I read several studies about how PhD students and postdocs suffer from depression. How can you not suffer from depression if you have to move every two years and all your personal relations are harmed by this? It is maybe at this point that women decide to compromise their career and choose to stay with their family.

But it is a complex problem and it’s not so clear how it would be possible to solve it in a fair way.