# PROF. RAFAŁ LATAŁA – FNP Prize Laureate 2023

### Professor Rafał Latała from the Faculty of Mathematics, Informatics, and Mechanics of the University of Warsaw received the 2023 FNP Prize in the field of mathematics, physics, and engineering sciences **for developing mathematical tools which led to the proof of Talagrand’s Bernoulli Conjecture**.

Professor Rafał Latała was born in 1971 in Warsaw. He graduated in mathematics from the University of Warsaw in 1994. At the same university, he later obtained his doctorate in 1997 and habilitation in 2002. Both his doctorate and habilitation were awarded Prizes of the Prime Minister. In 2009, he received the full professorship in mathematical sciences. In the course of his research career, he has completed numerous overseas internships and research visits, including to the School of Mathematics at the Georgia Institute of Technology in Atlanta, USA, the Department of Mathematics at the University of Connecticut in Storrs, USA, the Department of Mathematics at the University of Tennessee in Knoxville, USA, the Henri Poincaré Institute in Paris, France, the Fields Institute in Toronto, Canada, the Newton Institute in Cambridge, UK, and to and the Mathematical Sciences Research Institute (MSRI) in Berkeley, USA. Since 2009, he is leading the Department of Probability Theory at the Institute of Mathematics, University of Warsaw.

Latała is a member of the Warsaw Scientific Society, the American Mathematical Society, the Institute of Mathematical Statistics, the Polish Mathematical Society, the Association for Mathematical Education, and a member-correspondent of the Polish Academy of Sciences. For more than twenty years, he was a member of the Main Committee of the Polish Mathematical Olympiad, and in 2009–2016, he was its chairman.

Latała authored and co-authored more than 60 scientific articles, publishing in such journals as *Advances in Mathematics*, *Annals of Mathematics*, *Inventiones Mathematicae*, *Journal of Functional Analysis*, *Journal of the London Mathematical Society*, *Proceedings of the American Mathematical Society*, *Studia Mathematica*, and *The Annals of Probability*. He is editorial board member of the scientific journals *Studia Mathematica* and *Bulletin of the Polish Academy of Sciences: Mathematics*. He has repeatedly received prestigious scientific distinctions. In 1997, he received the Kazimierz Kuratowski Award for young mathematicians, and in 2002 he received the International Stefan Banach Prize of the Polish Mathematical Society (together with Krzysztof Oleszkiewicz) and the Sierpiński Medal of the 3^{rd} Division of the Polish Academy of Sciences, in 2007–2011 he received a professorial subsidy from the Foundation for Polish Science in the Master programme, and in 2014 he received the Prize of the Mathematical Institute of the Polish Academy of Sciences. In 2002, he was an invited speaker at the International Congress of Mathematicians in Beijing.

He specializes in probability theory.

Professor Rafał Latała from the Faculty of Mathematics, Informatics, and Mechanics of the University of Warsaw received the 2023 FNP Prize in the field of mathematics, physics, and engineering sciences **for developing mathematical tools which led to the proof of Talagrand’s Bernoulli Conjecture**.

Probability is the branch of mathematics that deals with random events. Among the objects that probabilists deal with are stochastic (random) processes used to model changes (usually over time) in random phenomena such as stock prices, a substance concentration in an experiment, river water levels, temperature at a fixed geographical location, the number of times a website is viewed, or the population size of a group of animals or plants. Random processes include the Bernoulli process, named after Jakob Bernoulli, a prominent seventeenth-century Swiss mathematician. The Bernoulli’s process deals with situations in which we study events associated with a numerous repetition of a single random experiment, which can end in one of two equally probable outcomes. For example, what is the chance of getting three tails in five coin tosses? Or what are the odds of having a series of fifteen consecutive heads in one hundred coin tosses?

For many years, one of the fundamental questions remained what is the maximum value of the Bernoulli process? At the end of the 1990s, the French mathematician Michel Talagrand formulated a hypothesis stating that “there are essentially only two ways to estimate the supremum (upper limit) of a Bernoulli process: one way is by the uniform bound and brutal adding of modules, and the other is by estimating supremum of the dominant Gaussian process.”

For the one who proves this hypothesis true, Talagrand has funded a prize of $5,000. However, before scientists can prove something in mathematical sciences, they must develop suitable mathematical tools for the specific purpose. This is what Rafał Latała has succeeded in doing. To prove Bernoulli’s hypothesis, Latała used and combined several sophisticated methods, including constructions of majorizing measures and related sequences of partitions, concentration inequalities, Sudakov-type minoration bounds, “greedy” induction algorithms, and maximum inequalities for sums of random vectors.

As a result of these efforts and the development of creative mathematical tools, Latała and Witold Bednorz presented a positive solution to Talagrand’s hypothesis for Bernoulli processes, reported in the world’s most prestigious mathematical journal *Annals of Mathematics* (180(3); pp. 1167–1203). Talagrand called the proof “simply stunningly beautiful.” Latała and Bednorz demonstrated the mathematical power, culture, and scientific achievements of the Warsaw School of Probability, which is one of the world’s leading probability schools.

The question raised by Talagrand’s hypothesis and answered by Latała is central to probability theory, statistics, and machine learning. The significance of this achievement goes far beyond its field and affects vast areas of pure and applied mathematics, as well as many other fields of science.

Both the result itself – i.e. the performed proof – and the very idea behind it are outstanding. The idea of the proof and the mathematical tools developed by Professor Latała for this purpose are non-trivial and may prove useful in solving many problems that we cannot even foresee today.

Fot. Magdalena Wiśniewska-Krasińska

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