02/09/2020

Dan Agüero defends thesis on Dirac Structures on Friday (4)

For Dan Agüero Cerna, undergraduate and master's degrees are academic stages in which "we broaden our knowledge". In the doctorate, expanding knowledge is also part of the process. But beyond that, it is necessary to have sufficient maturity to "contribute with something new", which requires even greater dedication. Next Friday (4), he concludes this challenge and defends his thesis "Complex Dirac structures with constant real index" via videoconference at 10:30 am. The presentation will be broadcast on IMPA's YouTube channel .

“ My research focuses on complex Dirac structures. To explain them, it's necessary to first discuss (real) Dirac structures. Mechanical systems are represented by Poisson manifolds; the constraints in these systems are submanifolds. A Poisson structure doesn't always descend to a submanifold and still remain a Poisson structure. What we obtained was a Dirac structure, so we can say that these are the objects that represent the constraints in mechanical systems.”

Dan further points out that the study of structures goes beyond mechanics and is a topic of study in itself, which he has been working on since the second year of his doctorate, when he studied generalized complete structures. "What motivates me is that perhaps, in the future, they will have some application in physics. Just as happens with generalized complex structures in theoretical physics."

Born in Ica, Peru, Dan was inspired by his aunt's career as a statistician to choose his undergraduate degree. At the Faculty of Mathematical Sciences of the National University of San Marcos, he had his first contact with pure mathematics and decided to become a mathematician. When he wanted to pursue a master's degree in the field, in 2014, he moved to Brazil and settled in São Paulo to study at the State University of Campinas (Unicamp).

“Since my undergraduate studies, I had heard about IMPA. We studied with books published by the institute, and I had some professors who also graduated from here,” says the doctoral student who has been at the institution since 2016. “The difference is the work environment, which allows for constant contact with researchers in the field.”

Throughout this stage, Dan was mentored by Henrique Bursztyn . “He gave me a certain independence for research. And he contributed a wealth of mathematical knowledge, full of key suggestions for my research. Sometimes I found myself stuck at a certain point, and in a quick conversation with him, it was already possible to get an idea of what was happening.”

The doctoral project was co-supervised by Roberto Rubio , who currently works at the Autonomous University of Barcelona. The two met when Rubio was doing his postdoctoral work at IMPA, and due to the proximity of the topic of Dan's thesis, the partnership arose spontaneously, generating good results.

Amid the pandemic, participating in video conferences has been an extra challenge for the doctoral student. “But we have no other option. At the time of the defense, for example, at least six people would be together in a cramped space, so it wasn't possible to do it in person. I also had to adapt the work I previously did at IMPA to work from home, something I had never done before. Just like many people during this time of social isolation, I also experienced some anxiety and uncertainty about the future. But I'm thinking about perhaps pursuing a postdoctoral fellowship in the field,” he points out.