25/06/2019

In the playing cards, the push towards Probability

The first time Roberto Imbuzeiro Oliveira, from Rio de Janeiro, heard someone talk about something that would become his professional choice was in a school class, back in elementary school. “The teacher said that there were doctoral programs in Mathematics. She explained that it was necessary to solve a problem that no one had been able to solve. I was impressed,” recalls the researcher, who has been at IMPA since 2006, where he holds a professorship in the area of probability.

On the path between being astonished by the professor's revelation and entering IMPA, Imbuzeiro encountered the Brazilian Mathematical Olympiad (OBM), a competition held since 1979 by the Brazilian Mathematical Society and IMPA. He says it was "by far the most difficult test" he ever took, considering what he knew at the time. He won an honorable mention, an achievement that literally put his future in his hands: as a prize, he received a book on combinatorics and probability.

Although she had attended math classes on Saturdays, when deciding on her undergraduate course she opted for Computer Engineering. With an excellent score on the entrance exam, she won a scholarship to PUC-Rio and joined a special class where math lessons were "excellent." "That's when a career in mathematics appeared as a possibility for me," she recalls.

During a college assignment, he ended up at IMPA to research curve length and surface area. Accustomed to the hustle and bustle of PUC-Rio, he initially found the quietness of the place strange, but he liked it so much that he decided to apply for a master's program. In his letter of intent, he specified dynamical systems, the research area of one of his favorite professors from his undergraduate studies, Lorenzo Díaz. At IMPA, he was supervised by Marcelo Viana, now the director-general.

Magician at the Brazilian Colloquium

The choice of Probability arose from conversations with graduate colleagues and visits to the IMPA library, where I found a book by my future doctoral advisor on probabilistic methods. The final push came from Persi Diaconis, a professor at Stanford University (USA), in a lecture on the Mathematics of shuffling cards, given at the 1999 Brazilian Mathematics Colloquium (CBM) at IMPA.

“He’s a very unique guy. He dropped out of school to become a magician and then went back to university and became a prominent researcher. I loved the lecture. At the end, he said: 'There are areas of mathematics where you spend five years just to understand the definitions. This field here is different. It involves algebra, combinatorics, probability, and anyone who wants to can study and discover things right now.' I looked into the subject and was fascinated,” says Imbuzeiro, citing Alexandre Belloni (Duke University), Andrea Montanari (Stanford University), and Gábor Lugosi (Barcelona Graduate School of Economics) as inspiring contemporary mathematicians.

Imbuzeiro completed his doctorate in Mathematics in 2004 at the Courant Institute of Mathematical Sciences, New York University. He chose the American Joel Spencer as his advisor after reading, at IMPA, the book "The Probabilistic Method," authored by Spencer and the Israeli Noga Alon, from Princeton University. "It was lucky that I chose the wrong method as my advisor and everything turned out so well," he says, who followed his doctorate with a post-doctorate at the IBM TJ Watson Center, also in the United States, supervised by Barbara Terhal.

Back in Brazil, forced to do so after receiving a government scholarship for postgraduate studies abroad, Imbuzeiro saw IMPA as the ideal place to establish his research career. “The international recognition, the exchange of people from institutions here and abroad, and the working conditions were appealing. Furthermore, I was a master's student there, and during my doctorate and postdoctoral studies, I came to IMPA several times. I thought I could be happy here.”

With three children, aged 7, 9, and 12, and married to an IBM researcher in Rio, Imbuzeiro was right. Today he supervises five doctoral students, three master's students, and conducts research in probability and its relationship to problems in statistics, discrete mathematics, and quantum information, among other areas. He was previously the manager of the Teaching and Planning and Projects divisions at IMPA .

As an example, he cites a more recent study, in partnership with Yuval Peres and Anna Ben-Hamou. The three focused on "the large social networks that dominate our lives," more specifically Facebook, so large that it is impossible for it to exist in the memory of a single computer. Translated into "a naive question," the mathematical problem in question would be: What can you learn about a very large network by only looking at a piece of it, through a random stroll?

“The study we conducted was to see, under what conditions, from a really short browsing session on Facebook, you can obtain some kind of global information about the network. There are many other things that can be studied as well. Like almost everything in mathematics, you discover one thing and, immediately, other things appear as a natural progression of what you discovered.”