Letícia Mattos defends thesis on combinatorics.

Crédito: Arquivo Pessoal

Counting is part of Letícia Mattos' life in many ways. Besides being the name of the city where she was born and lived, in the Metropolitan Region of Belo Horizonte, counting is what she does within her research area, Combinatorics. "During childhood I already had the idea that, whatever the profession, it should involve mathematics. Today, mathematics represents my life. I can't imagine myself without it," she summarizes.

About to receive her doctorate from IMPA, Letícia will present, next Friday (11), at 10 am, the thesis “Combinatorial Properties of Random Graphs and Matrices”, supervised by Professor Robert Morris. The presentation will be made via videoconference and will be broadcast on the institute's YouTube channel .

In short, the researcher explains what is studied in Combinatorics. “Is it possible that, in any sufficiently large group of people, there are 'k' people who are friends simultaneously or 'k' people who are not friends simultaneously? We know, for example, that in any group with more than 48 people, there are 5 people who are friends simultaneously or 5 who are not. However, to this day it is not known whether in any group with 47 people it is possible to guarantee this property. We don't understand this problem very well for very large values of 'k'.” In mathematical language, these groups along with their friendship relationships are known as graphs. “In general, we seek to find certain structures in graphs, count graphs with certain properties, and analyze the behavior of random graphs,” she says.

The teachers she had throughout her school years were fundamental in her choosing mathematics as a profession, shares the Minas Gerais native. "They noticed my interest in mathematics and always encouraged me to continue studying." Participation in the OBMEP (Brazilian Mathematics Olympiad for Public Schools) also played an important role in her relationship with the subject, introducing her to "a completely unknown universe." In the meetings of the Junior Scientific Initiation Program (PIC Jr.), she was able to learn mathematics "in a light, enjoyable, and at the same time challenging way."

Her interest in Combinatorics arose during her undergraduate studies in mathematics at the Federal University of Minas Gerais (UFMG), where she also earned her master's degree. But it was during a summer course at IMPA in 2013 that she became even more fascinated by the field, she says. The beginning of her doctoral studies in 2017 was not without some difficulties. “There is a huge universe between mathematics in textbooks and mathematical research. I really learned about research in the seminars organized by my advisor, Rob Morris. I believe that this was fundamental to my academic growth.”

Working in a field that is still predominantly male, the doctoral candidate found support in other female researchers at the institute. “I have always looked to researcher Carolina Araujo as an inspiration. In addition to being an excellent mathematician, she has contributed significantly to discussions about gender disparity in mathematics and science in general.”

Letícia is already planning the next steps in her career. After her doctorate, she will do a post-doctorate at the Freie Universität Berlin, one of the most prestigious universities in Germany and Europe, and another in the United States, at the University of Illinois.