19/05/2020

Luiz Paulo Moreira defends his thesis on random graphs.

About to complete a decade at IMPA, doctoral student Luiz Paulo Moreira rehearses his farewell to the institute from which he also holds a master's degree. This Friday (22), at 2 pm, he defends the thesis “A walk through random graphs” by videoconference, concluding the course. In the work supervised by researchers Robert Morris and Roberto Imbuzeiro, Luiz Paulo addressed the extremal properties of random graphs.

The branch of mathematics he studies is combinatorics, specifically objects called graphs, which are a very simple abstraction of a symmetrical relationship, explains the doctoral candidate. "A symmetrical relationship between a pair, of people for example, is any relationship where the order doesn't matter." As an example, he cites an everyday gesture: a handshake. "If I shook your hand, you shook mine too."

With a simple structure formed by points and lines connecting them, graphs are the subject of study for an increasing number of mathematicians. Luiz Paulo points out that some seemingly simple questions about them can be difficult to answer. A good example is Mantel's Theorem, which can be stated based on the symmetrical relationship of dating. "If I date someone, that person also dates me. In a group of n people, how many relationships have to happen to ensure there is a love triangle, with three people dating in pairs?"

Born and raised in Fortaleza (CE), Luiz Paulo considers that he had a typical childhood, surrounded by friends, cousins, and uncles. With a "giant family"—his father has eight siblings and his mother has six—he lived in a lively and cheerful house, with lots of games. He considers writing his own name at the age of three to be the greatest academic achievement of his life. "My mother, who is a teacher, still keeps the paper to this day," he says.

It was at her grandmother's house that she immersed herself in books and music, developing a personal taste. "I discovered 'the obsession' of really liking to think and delve deeply into a single thing." At the Military Police College of Ceará, where she spent most of her student life, she participated in extracurricular activities such as soccer, horseback riding, synchronized marching, and choir.

With so many interests, he admits that mathematics wasn't exactly a choice. "I prefer to believe it was chance." Participation in science olympiads may have been the starting point for his interest in the field. His good performance in the competitions earned him a place in an elite school in the region. "I devoured all the new olympiad classes and did well. The school specialized in positive reinforcement, so I fell in love with it in a mix of ambition for the awards and for learning more. Of all the obsessions I've had, this must have been the one that went the furthest. I studied about 12 hours a day of mathematics and didn't see the time go by."

He ended up in the mathematics undergraduate program at the Federal University of Ceará (UFC), where he considers that he was "intellectually formed." The solid background in mathematics, which he says was a legacy of participating in Olympiads, facilitated the adaptation process, he says. He embarked on his first Summer Program at IMPA in his second year of undergraduate studies. "It was a memorable experience in many ways."

Enchanted by his summer experience, he decided to pursue a master's degree at IMPA. During the course, he had the opportunity to meet researcher Roberto Imbuzeiro, whom he considers a "guru." "Among so many conversations, both mathematical and non-mathematical, he was the one with whom I had my first contact with probability and discrete mathematics," he points out. He also became close to Roberto Morris and Hungarian combinatorics, his favorite subject. "The two of them are a big part of why, within mathematics, I study combinatorics."

Since then, dedicated to studying the area, Luiz Paulo feels that graphs compel him to "get his hands dirty." "In contrast to more classical areas, proofs in combinatorics are much more artisanal. I like the freedom that comes with that."

Alongside his mathematical research, the doctoral student leads a busy life, constantly embarking on new activities. Since moving to Rio de Janeiro, he has taken courses in visual arts at the Parque Lage School of Visual Arts, animation at Anima Mundi (where he also led workshops), climbing, German language classes, and parkour. But what gives him the most pleasure in his free time are conversations with friends, which prevent him from "settling into the act of thinking," and the classes he teaches in the social projects "Pré-vestibular do Cerro Corá" and "Prepara Nem." "These have often been the highlight of my week. Going up the hill, managing to teach things they were sure they wouldn't learn, making friends, and then coming down the hill."

In the final stretch before completing his doctorate, the Ceará native is confident. “I was strongly encouraged to become a more independent researcher, and I’ll be finishing my doctorate with several collaborators,” he comments. Even though he doesn’t like to think about the future, he followed the unanimous advice of his colleagues and professors and applied for postdoctoral programs, being accepted at the Pontifical Catholic University of Rio de Janeiro (PUC-Rio). “What I know for now is that I will remain close to IMPA,” he says.