21/10/2022

'IMPA is thriving and becoming increasingly important,' says Avila.

Complex and meaningful drawings for those who explore the area of dynamical systems in depth adorned the scene during Artur Avila's lecture, this Friday (21). Closing the “IMPA 70 Years Conference”, the extraordinary researcher and winner of the Fields Medal in 2014, presented a discovery by Henri Poincaré, from the end of the 19th century. Avila's career has been marked by IMPA and, in turn, he was one of those responsible for raising the institute's level of excellence.

“Since I joined IMPA, we have already celebrated 50, 60, and now 70 years! It’s wonderful to see that things continue to move in the right direction. IMPA has been successful for a long time, even before I started. Sometimes things are fragile, so it’s good to see that the institute persists and has this continuity, despite any difficulties it may face. IMPA thrives and is becoming increasingly important,” stated Artur Avila.

The presentation focused on dynamical systems, Avila's area of expertise. Even before beginning his lecture to the packed auditorium, he recalled one of his first visits to IMPA, when he heard researcher Carlos Gustavo Moreira speak on this same topic. "At the time, I was just starting my studies here and didn't have the capacity to fully understand research like this," he commented.

Mahler's conjecture and billiards

Vinícius Ramos apresentou a conjecutra de Mahler

Also participating in the “IMPA 70th Anniversary Conference” was IMPA researcher Vinícius Ramos. He explained how a more recent conjecture, Viterbo's conjecture, is implicated in Mahler's conjecture, which is over 80 years old. The researcher also showed the connection that symplectic geometry has with billiard theory.

With a doctorate from the University of California, Berkeley, in the United States, a post-doctorate from the University of Nantes, France, and an excellent post-doctorate from IMPA, Ramos began a new challenge this year: he was selected by the IAS (Institute for Advanced Study), which Albert Einstein helped found in 1930.

The researcher, who has already completed five years at IMPA, will spend his sabbatical year at the new institute continuing Viterbo's line of research and deepening the understanding of problems involving billiards.

"It's a place of Pure Science, it doesn't have a laboratory. A place for mathematics, physics and human sciences, where knowledge is explored to the fullest and they provide all the physical conditions so that you don't have to worry about anything else," the researcher said enthusiastically.

At the institute, Ramos will continue Viterbo's line of research and the understanding of billiard table problems.

"My biggest dream is to demonstrate new things," he concluded.