26/01/2024

Danielle Nunes defends her doctoral thesis at IMPA.

It was in high school that Danielle Nunes was hooked by mathematics. Several times challenged to choose another path, she remained firm in her choice and is now reaping the rewards of another stage. Danielle will defend, next Tuesday (30), in room 232 of the institute, her doctoral thesis “Commensurability and mutations of hyperbolic polyhedra”, with transmission via IMPA’s YouTube channel from 1 pm.

Under the guidance of IMPA researcher Mikhail Belolipetsky, Danielle used Coxeter maximal decompositions of polyhedra to prove that in the case of two non-arithmetic polyhedra, when their maximal decompositions have different volumes, they cannot be commensurable. She also explored the application of this result to answer an open question about the commensurability of certain pairs of mutant polyhedra.

"During the research, we sought a commensurability invariant that wasn't one of the already known algebraic ones. We found a geometric commensurability invariant, and during the process, we also found two other results that are consistent with the theory. We also obtained two other results, and we created a definition to generate a path for the sequence of paths in this cycle of definitions," explained Danielle.

Holding a degree in mathematics (Bachelor's and Licentiate) from UFF (Federal Fluminense University) and a Master's degree from the same university, Danielle had already participated in IMPA's Summer Course, and her choice to pursue a doctorate here stemmed from her familiarity with the Institute's excellence. "For me, IMPA is a national symbol of the prestige of mathematics, and the facilities here are fantastic," she said. "I was always told that doing a doctorate at IMPA would be extremely difficult, so being here is a dream come true," she added.

She says that her family's view of mathematics was transformed after IMPA researcher Artur Avila won the Fields Medal. "When Artur won the Fields Medal, my family's notion of mathematics changed a lot, and at that point I was already finishing my undergraduate degree. So, it was great, as a mathematician, to see this change in perspective," Danielle said.

When she was in school, she already had a curiosity and interest in the fundamentals of mathematics. The desire to understand the 'why' of logic in the subject made Danielle increasingly interested in mathematics and its patterns. Despite this, she says that even her math teachers, while recognizing how good she was at the subject, suggested that she try another path. "My physics teacher even gave me one of her books and asked me to choose some kind of engineering."

Furthermore, Danielle has worked correcting exams for the OBMEP (Brazilian Mathematics Olympiad for Public Schools), and she loved following the development and interest of such young students in mathematics.

"It's great when I can, in some way, convey to people in my family, for example, what I do. Being able to make people who don't understand, understand the subject is something I enjoy," Danielle concluded.

The young woman even plans to combine her research career with teaching in the future (although she doesn't yet know if she will teach at the primary or higher education level), since she enjoys and feels happy explaining complex mathematical topics in a simple way.