15/04/2024

OBMEP medalist defends doctoral thesis at IMPA.

Originally from Sergipe, IMPA doctoral student Lucas Aragão categorically states that the OBMEP ( Brazilian Mathematical Olympiad for Public Schools) was a turning point in his life. His first medal, won in 2009, secured him a place in the PIC (Junior Scientific Initiation Program) , which offers advanced mathematics classes for students awarded in the Olympiad, and also in a regional course called "Young Talents in Mathematics Project". These programs not only helped Lucas win four more medals in the OBMEP, but were also decisive in his choice to study mathematics.

“I won three gold medals and two silver medals in total, but I was also awarded prizes in the computer science, astronomy, and physics olympiads, and later in the University Mathematics Olympiad. I am a product of OBMEP. It opened enormous doors for me. I liked mathematics since I was little, but OBMEP was a turning point in my life. That's where my interest in pursuing a degree in mathematics came from ,” he says.

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Encouraged by the guided study program, Lucas was accepted into the mathematics program at the Federal University of Sergipe (UFS) in 2014, while still in his first year of high school. It was also during his first year at university that he decided to participate in a Summer Course at IMPA.

“I really enjoyed the Summer Course, I really liked Rio de Janeiro and I wanted to finish my undergraduate degree quickly and start my master’s degree here at IMPA”. And so it was done. Lucas not only completed his master’s degree at the institute but also finished his doctorate this Friday (12).

With his thesis “Some problems in Extremal, Additive and Probabilistic Combinatorics”, Lucas dedicated himself to investigating five problems in different areas of combinatorics. Under the guidance of Robert Morris, the student explains that the thesis was divided into six chapters. In one of them, the student asymptotically determined the minimum number of monochromatic solutions of the equation xy=z for any 2-coloring of the interval {2,…,N}, among other points. “Combinatorics is the area of mathematics that studies discrete objects, and one of the questions is: what are the sufficient conditions to guarantee the existence of a certain structure? Another question is: given a structure, how many of these objects can we find? So, one of the main problems I tackled in this thesis was answering the question: what is the minimum number of monochromatic solutions to the equation xy=z that we can guarantee any coloring of the integers from {2, …,N}. We colored the integers from 2 to “N” with “R” colors and asked: how many monochromatic solutions can we guarantee that the equation has?”, explained the student.

Lucas's thesis defense was broadcast on IMPA's YouTube channel last Friday (12). Now a doctor, he intends to secure a research position at one of Rio's public universities. Lucas already works as a substitute professor at UFRJ (Federal University of Rio de Janeiro).