03/06/2025

From Physics to Mathematics: Deborah Oliveira defends her doctoral thesis.

A graduate in Physics from UFMG (Federal University of Minas Gerais), where she also completed her master's degree, Deborah Oliveira found in IMPA the opportunity to change fields and delve deeper into Probability – a field she has always been interested in. Originally from Contagem (MG), the doctoral candidate explains that the transition was motivated by the search for a mathematical rigor that she did not find in her previous training.

“During my undergraduate studies, I already preferred Quantum Mechanics, Statistical Mechanics, and Thermodynamics—areas that fundamentally involve probability. During my master's degree, I became more familiar with research, and the lack of mathematical rigor bothered me, so I decided to come to IMPA.”

Now, the doctoral student is preparing to defend her thesis “Detection and counting of communities in weighted random graphs”, which was supervised by the institute's researcher Roberto Imbuzeiro. The research presentation will be next Thursday (5), at 9:30 am, in room 232 of IMPA. The thesis defense can be followed on IMPA's YouTube channel.

“This thesis investigates properties of the adjacency matrix of weighted random graphs. We study the community detection problem, and in more detail, the problem of estimating the number of communities in a stochastic model of weighted blocks in the degree-diverging regime. Using hypothesis testing, we construct a consistent sequential estimator capable of identifying the true number of communities. We also construct estimators for the communities themselves. We use a method based on semidefinite programming that performs better than other methods in the quasi-sparse graph regime, such as the spectral method, for example,” summarizes the doctoral candidate.

The daughter of an administrator, Deborah says her love for mathematics began when she was still a child. “My father always encouraged me. I remember him giving me math games and magazines. I also liked doing calculations, but I don't think he imagined what it would lead to. He's very happy and tells everyone that I'm doing a doctorate,” she said.

With her family proud of her journey, the student is now preparing for a new step: Deborah will go to Canada to pursue her postdoctoral studies at McGill University. This achievement represents another reason for celebration for the family and another change in her research focus. “In my doctorate, I can say that my focus was on random networks. In my postdoc, I will apply random matrix theory to machine learning ,” she explained. This new academic phase also builds on the practical experience gained between November 2023 and December 2024, when Deborah was part of Petrobras' seismic inversion project at the Pi Center (IMPA's Center for Projects and Innovation).

“It was a very enriching experience. I had the chance to closely observe the workings of a machine learning project, in addition to developing applied research in the area,” she said. For her, this practical knowledge will contribute to her postdoctoral studies, which will now have a more theoretical focus, exploring the use of random matrix theory in machine learning problems.