Cayo Dória defends his thesis and dreams of making a living from mathematics.

The examples from childhood have a great impact on people's lives, even when, as adults, they choose a particular path. This was no different for Cayo Rodrigo Felizardo Dória. Originally from Aracaju (SE), he barely remembers when he started to like mathematics. He believes his appreciation for the subject arose when he noticed "the obvious pattern in the multiplication table of 5, going through the pleasure of solving systems of linear equations that modeled simple everyday problems, and the fascination of discovering the abstract/pure side of mathematics in his undergraduate studies, in basic courses such as linear algebra and analysis of the real line."

The inspiration to become a mathematician came from home. His mother's cousin, whom he called "Uncle Danilo," had a career in the field as a researcher at UFPE (Federal University of Pernambuco) and UFS (Federal University of Sergipe). Dória looked up to him.

"I combined my love for mathematics with the prospect of being able to make a living from it, based on this example," he says.

In addition to family influence, the student from Sergipe also had excellent teachers during his high school studies at CEFET-SE (now IFS). From there, he went on to study at UFS during the same period as the start of Reuni, a program to expand the federal university network.

“I saw the university basically double in size during that period and I was thrilled by that environment of encouragement for science. I remember that when I did my first scientific initiation with a former IMPA student [Almir Santos], I was one of the few pure mathematics students to have that privilege at UFS. Before, students could only get rare scholarships with physics or engineering professors. Over time, the number of scholarships for mathematics has been growing. This certainly motivated me to continue and pursue postgraduate studies,” he says.

Encouraged by the success of good UFS students at IMPA, he decided on his next steps. First, he participated in the summer course in his final year of undergraduate studies. Subsequently, he was accepted into the master's program.

“I’ve been at IMPA since 2012. I gained most of my mathematical knowledge here,” reveals Dória.

Almost a reality…

The next challenge for the Sergipe native who dreams of making a living from mathematics is his thesis defense, at 11 am on July 18th. Supervised by Mikhail Belolipetskiy, his work is in the area of Geometry. To be more specific, we can say it deals with "Geometry and Topology in low dimensions." Not very fond of these nomenclatures and divisions, Dória simply says that he "does Mathematics," and that's it!

The thesis addresses a rather theoretical question about a space formed by Riemann surfaces, also known as moduli space.

“Within it, I have a very special subset known as the subspace of arithmetic Riemann surfaces. There are some peculiarities of this subspace that give rise to a mathematically very natural and interesting question, which is how they are distributed within the larger space. My thesis aims to try to obtain some answers to this question. We can say, based on my thesis, that the subspace is neither uniformly spaced nor concentrated in a small area. It is still a very interesting mystery to learn about these special objects. Especially since arithmetic Riemann surfaces have some relevance in computing and number theory,” he explains.

The question remains: does all this have practical application? The doctoral candidate says that, although the topic studied has connections to practical applications, that was not his focus.

"Actually, what I like most about my work is the application of mathematics to mathematics. To study a geometric problem, I applied ideas and results from combinatorics, complex analysis, group theory, and number theory, to name a few examples. I think the greatest contribution to academia is yet another demonstration of the integration between the most diverse branches."

The choice of Belolipetskiy as advisor is directly related to Dória's opinion that Mathematics should not be divided. Thus, when he had to choose a direction for his doctorate, he opted for the researcher. "His work contained topics in Mathematics that I have always been interested in."

From acceptance to guidance, the two built a great relationship, especially because Belolipetskiy encouraged the student to study quite diverse subjects.

“It was also a privilege to be part of the lineage of Russian mathematics, one of the schools I admire most in the modern history of mathematics. From a personal point of view, Mikhail was always an unconditional supporter. Because of his experience, it was always comforting to heed his suggestions.”

According to Dória, the environment at IMPA is very stimulating and offers students the chance to meet "mathematically brilliant people," in addition to exchanges with international centers.

After defending his thesis at IMPA, he already has a guaranteed postdoctoral position at USP (University of São Paulo). After that, it's just a matter of packing his bags and living… the dream of mathematics.

SERVICE:

Defense of thesis by Cayo Rodrigo Felizardo Dória

"How systoles increase"

Date: July 18th | Time: 11:00 AM | Location: Room 236