Interview with Oleg Lepski, invited speaker at ICM2022

Link to the virtual ICM 2022 talks

What is your field of study?

My research interests are mathematical statistics and related questions in probability theory and functional analysis. One of the main subjects is the theory of adaptative estimation. The essence of the adaptative approach can be described in general like this: imagine that we are interested in a certain problem, whose optimal solution might be obtained under several hypotheses (also called conditions). Often (and this is the main difficulty) the optimal solution depends on the conditions under which it has been obtained. On the other hand, it is rare that we know in advance which condition among all the possible corresponds to the reality. And then we arrive at the main problem of adaptation: is there (and if yes, how to find it?) a unique solution that will be simultaneously optimal for a broad range of conditions?

What led you to take up mathematics?

It is hard to say exactly what led me to do maths, but I have had an interest in the subject since I was very young. If I remember correctly, at 11 years old, I took part in the mathematics Olympiad in one of the districts of Moscow and I came second.

How would you describe your profession?

Probably, like every other creative job: intense mental work, sometime painful, and a euphoric moment when the solution is found.

What do you like about being a mathematician?

In a word, freedom. It seems to me that that is inherent in any creative activity: freedom to choose the kind of work and how you do it.

What is a “profound” result for you?

For me, the significance of a mathematical finding is chiefly linked to the number of new techniques “invented” for its proof.

Have you already decided what you will talk about at the ICM?

Yes, I’m going to talk about a new, completely abstract, adaptative estimation that can be used in different statistical models.