02/04/2019

Catalina Freijo's thesis investigates exponents of Lyapunov.

Argentina from Mar Del Plata, Catalina Freijo grew up playing with clay, paints and other forms of artistic expression. She believed that the future was already there. But as Mathematics was also a stimulus at home, it is not surprising that she is about to complete a doctorate in the area. The thesis defense will be this Wednesday (3), at 5 pm, in room 236 of IMPA.

Looking back at Catalina's childhood, now at age 27, can help in understanding the journey she took between seemingly very different areas. At the time, Catalina's parents, an architect and a biologist, transformed homework time into such a pleasant family moment that it remains a highlight in her fond memories. Like her two siblings, she was also motivated to explore various fields of knowledge, including mathematics.

“My parents used to sit with us to do our schoolwork, and they did it in a very loving way. I think that's passed down from generation to generation. When someone shows you something and says, 'Look, this is fun,' like they did, it's different. With math, there's an eternal taboo, right? There are videos on the internet that show how parents explain math to their children, and it's very violent sometimes. Parents, when they're bad at math, sometimes say, 'I didn't like it, you're going to be like me.' That can be a very important obstacle. Often, the child only gets as far as the parents' successes,” she observes.

From her parents, she also learned to see the connection between different areas of knowledge. Therefore, she moves with ease between different fields of knowledge: researching mathematics, painting, dancing… And when faced with the question about the application of her thesis entitled "Continuity of Lyapunov exponents for linear cocycles with only one holonomy," she seeks the answer in art: "What is the purpose of music?"

In her work, supervised by IMPA's director-general, Marcelo Viana, she presents a partial result for his conjecture that only a uniform holonomy is sufficient to guarantee the continuity of Lyapunov's exponents.

“We work with continuity, which is more or less a way of explaining the rate of expansion and contraction of a system that has evolved over time. In general, all of this is based on gas theory. So, you have particles that move. If these particles are expanding in one direction or another, if they rotate, what happens? If two systems are always close, will they, for example, have the same rate of expansion? Will they always remain close?” he explains.

Catalina experienced the chaotic movements so common in dynamical systems, the area she chose to study, both inside and outside academia. After graduating from the Universidad Nacional de Mar Del Plata – a “small, familiar” environment where everyone knew each other – she left her hometown for one of the world's leading mathematical research institutes, with a high level of prestige and competitiveness. “When I started here, I was the only woman in the class,” she recounts, emphasizing how alone she felt.

Thesis dedicated to women mathematicians.

The demanding routine, common to doctoral programs, contributed to new challenges. Besides her mother, who came to Rio to stay for a while, Catalina could count on Viana. “He gave me a lot of support during that time. Whenever I had any difficulties, he was there to help,” she recounts, also highlighting the role of Karina Marin, an Argentinian who completed her doctorate at IMPA, also under Viana's supervision, and is now a researcher at the Federal University of Minas Gerais (UFMG). After the qualifying exam, she became Catalina's co-supervisor.

“I spoke with Marcelo about her. He agreed,” she says, emphasizing the importance of diversity in mathematics as well. “The gender issue in the field is still discouraging, although there is more encouragement for this inclusion nowadays,” assesses Catalina, who dedicated her thesis to women mathematicians.

In addition to the low representation of gender in Mathematics – “it’s important to know that you are not alone” – the Argentinian researcher considers it relevant to discuss the issue of mental health in academia, a problem that, according to her, affects everyone, regardless of gender.

“Often, we look the other way to pretend there isn’t a pink elephant in the room, but this is important. Many of us are suffering and battling with this. And if you are a woman, you are more likely to experience it. There are studies on this, it’s not just me saying it.”

After completing her undergraduate degree with a doctorate, she wants to take a vacation right after defending her thesis. She intends to stay in Rio and continue her research, which combines art and mathematics.

SERVICE:
Thesis defense by Catalina Freijo
"Continuity of Lyapunov exponents for linear cocycles with only one holonomy"
Date: April 3rd | Time: 5 PM | Location: Room 236