“I’m proud of what I’m accomplishing,” says Igor Blatt

“I’m proud of what I’ve been able to achieve.” At 29, Igor Alarcon Blatt is about to defend his doctoral dissertation at IMPA. The son of a homemaker and a salesman, a public-school student, and the first member of his family to pursue an academic career, he will present, next Friday (the 11th), the thesis “Classification of Admissible Low-Growth W-Algebras,” advised by IMPA researcher Jethro van Ekeren. The defense will take place at 10 a.m. in Room 232 of the Institute, with a live stream on IMPA’s YouTube channel.

The path that led the mathematician to his doctorate began in childhood, in Cachoeiras de Macacu, in the Rio de Janeiro Metropolitan Area. Before considering a career in mathematics, Blatt had other plans. Like many children, he wanted to be a soccer player. Then he thought about becoming a drummer in a rock band. Later, he developed an interest in engineering, along with a fascination with building robots.

Math, however, was always a part of his life. Blatt was a good student, and among his school subjects, one stood out. “Math was always what I found most fun,” he says.

It was this passion that led him, at age 11, to participate for the first time in the OBMEP (Brazilian Public School Mathematics Olympiad). In his debut, he received an honorable mention. The following year, he won his first bronze medal.

More than just an award, OBMEP introduced the young man to a world he had not yet discovered. Through the competition, he was invited to participate in PIC Jr. (Junior Scientific Initiation Program), an initiative that brings medal-winning students closer to mathematics and research.

“It was at PIC that I discovered that mathematics could be a career,” he recalls. Until then, Blatt had simply enjoyed math as a student. At the program’s meetings, he got to know people who were studying and working in the field. “I learned that there were careers in math and that I could pursue one someday.”

In his senior year of high school, Blatt once again won a bronze medal at OBMEP. Even so, he hadn’t completely decided to pursue mathematics.

When it came time to take the college entrance exams, Blatt chose Control and Automation Engineering at UFRJ (Federal University of Rio de Janeiro) and Mathematics at UFF (Fluminense Federal University) as his second choice. “I said, ‘I’m going to take one semester of math. And if I like it, I’ll stay. If I don’t like it, I’ll try to get into engineering again.’ And then, right in the first semester, I fell in love with it.”

In college, he discovered a different kind of mathematics than what he had known in high school—and, to him, it was even more interesting. His passion for the field was matched by his dedication. Living in Cachoeiras de Macacu, he commuted daily by public transportation for four hours to Niterói.

Throughout his undergraduate studies, he became interested in representation theory, a field that would later lead him to the study of vertex algebras. Upon completing his undergraduate degree, he began taking graduate-level courses—also at UFF—and started conducting research.

In 2022, as he was finishing his master’s degree, Blatt attended an event at IMPA on vertex algebras and decided to apply for a Ph.D. Before visiting the institute, Blatt had imagined he would find a place characterized primarily by competitiveness. He found something different. “People help each other a lot; they cooperate a lot with one another. And it’s very hard to find anyone who isn’t kind to you,” he says.

A thesis at the intersection of mathematics and physics

The research conducted at IMPA falls within the field of algebra, more specifically in the study of so-called vertex algebras. These mathematical structures emerged in connection with problems in mathematical physics and representation theory. Over time, they have also established connections with fields such as string theory and quantum field theory.

Within this field, Blatt studied what are known as affine W-algebras. The research seeks to understand and classify a specific class of these structures based on properties related to the behavior of their characters—mathematical objects that encapsulate information about the representations of an algebra. Thus, the goal is to understand how certain pieces of information associated with these structures behave as they grow and what conclusions this allows us to draw about the algebras themselves.

To investigate the problem, Blatt worked with explicit formulas for so-called asymptotic data and with combinatorial tools related to nilpotent elements. The result was a complete classification of a class of admissible W-algebras. The research also made it possible to identify these structures as finite extensions of minimal Virasoro models, an important class within vertex algebra theory.

Although he works with highly abstract and specialized concepts, the mathematician views his thesis not only as the solution to a specific problem, but also as a starting point for new questions. During the research, examples and ideas emerged that were not ultimately incorporated into the final work but that can continue to be explored. “The thesis was a place where some cool ideas blossomed that I can continue to work on in the future,” he says.

The plan is to continue investigating these issues in collaboration with Jethro over the coming months. Looking ahead, Blatt is considering options such as a postdoc or an academic career.

His thesis defense marks the end of a journey that, for him, represents much more than an academic degree. It is the culmination of a path that began at a public school in Cachoeiras de Macacu, continued through OBMEP, and involved overcoming countless personal challenges. “When you look around, you realize that it’s not easy for someone who came from a public school—who faced various financial problems with his family and everything—to get to a place like this. I’m happy and proud of the journey I’ve taken so far.”