11/03/2021

The non-linear trajectories of João Fernando Nariyoshi

“Non-linear” paths had already crossed João Fernando Nariyoshi’s life, even before he understood the mathematical meaning of this classification common to equations. The choice of professional career had an unusual path: theology, philosophy and physics were some of the possibilities he considered pursuing. And only after a brief stint in the basic engineering course at the University of São Paulo (USP), did he decide to definitively throw himself into the field of mathematics. On Friday (12), he defends the thesis “Lemmas and applications of average speed”, in pursuit of the title of doctor at IMPA. The presentation will be broadcast on IMPA’s YouTube channel .

In his work, Nariyoshi introduces a method capable of establishing average speeds for a wide range of parabolic-hyperbolic equations. He then applies these lemmas to prove new results concerning nonlinear problems. He also contributes a general method for studying non-degenerate stochastic problems, as well as a study on the smoothness of solutions for a parabolic-hyperbolic problem. For this, he was supervised by Professor Hermano Frid.

“Linear equations are those that satisfy the principle of superposition. Imagine a lake with water; if you throw a stone, you create waves on the surface. If you throw another one immediately afterward, it's as if the water's surface is the sum of the waves. But this isn't necessarily always true. If you don't throw a pebble, but a rock, it's very different,” he explains. In his studies, Nariyoshi moved from the microscopic to the macroscopic context to develop a mathematical technique that can be applied to certain problems, exploring the behavioral field of solutions.

Since the beginning of the coronavirus pandemic in March of last year, the São Paulo native left Rio de Janeiro, where he had lived since 2017, and moved to his father's house in Brasília. “In a way, the change was positive. It took me many months to reach the results I obtained in my thesis. It was a huge accumulation of work until I arrived at something final, and I really don't know if that would have been possible if we were back to the normal pace of life. In some ways, I can say that the quarantine brought me focus,” he explains.

Nariyoshi also cites as inspiration a lesson he takes from Leo Tolstoy's book "War and Peace." "One of the characters, who had been a prisoner of the French, believes he learned much more from suffering than from prosperity. It's clear that the pandemic isn't a good time for anyone. But perhaps that's partly it: we are learning many things."

Born in São Paulo, Nariyoshi spent his childhood and adolescence in the capital, more precisely in Vila Mariana. During his engineering studies at USP (University of São Paulo), he realized he enjoyed calculus and linear algebra classes more. That's when he changed fields. "You only live once. There, I bet all my chips on mathematics." At the end of the course, he received an honorable mention from the university as the best student in his class and immediately began a master's degree, also at USP, in applied mathematics.

“At USP, I continued with the same advisor, Professor Orlando Lopes. He taught me almost everything I know about mathematics and recommended that I come to IMPA. I thought I wouldn't be good enough to be at the institute, but he encouraged me a lot, and it worked out,” he says.

Confident, he went to Rio de Janeiro, a city previously unknown to him, to pursue his doctorate. “IMPA is a dream place to work and study. As a good São Paulo native, I didn't imagine there would be such an environment in Rio de Janeiro. In fact, I didn't believe anything similar existed anywhere in Brazil. I will miss everything very much, including Beto, the IMPA restaurant, with whom I became very good friends.”

And for the coming years, the future doctor prefers not to anticipate. “If I knew what I was going to do in the next stages of my life, I would already be doing it now, without a doubt,” he exclaims, good-humoredly. But he anxiously awaits the results of postdoctoral fellowship applications. “Any kind of planning has become impossible in this moment we are living through. But also, as it says in the book 'War and Peace', while there is life, there is happiness. There is a lot ahead, a lot.”