Ivan Passoni defends his thesis in the area of minimal surfaces.
“One of the biggest fears of graduate students in Mathematics is knowing whether the problem their project proposes is real and whether there is a solution for it that can be discovered with the time and knowledge available at this stage of academic life,” says Ivan Passoni, a doctoral student at IMPA.
One day before defending his thesis, this is a concern that the mathematician can already dismiss. This Friday (5), at 1:30 pm, room 232 will be occupied by the examining board composed of six researchers ready to debate the work “Construction of genus one helicoids in $mathbb{H}^2 times mathbb{R}$ ”, authored by Passoni and supervised by researcher Harold Rosenberg.
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Belonging to the field of minimal surfaces, within the area of differential geometry, the doctoral candidate's thesis relates to one of the elementary questions in this field: Plateau's problem. Developed in the 18th century, the question posed by the Italian mathematician Joseph-Louis Lagrange and later named in honor of the Belgian physicist Joseph Plateau sought to find the surface of smallest area that has a given boundary.
The problem can be illustrated with a simple, everyday image. Take a piece of wire and shape it however you like, as long as you join its two ends at the end. The question raised by Lagrange sought to understand precisely what the smallest surface area would be that would have this wire as its boundary.
The experiments conducted by Plateau showed that the desired surface can be imagined as the soap film we obtain if we dip our wire into a solution of water and soap.
In Passoni's work, the type of surface studied is in non-Euclidean spaces. In his doctoral thesis, the mathematician dedicated himself to constructing a minimal surface in a space of non-positive curvature. Similar to a helix, the developed figure also has a handle.
It is with this contribution that the mathematician bids farewell to IMPA. Commenting on his time at the institution, Passoni praises the scientific and research environment and the excellence of his doctoral colleagues, researchers, and professors. But another factor, not at all academic, makes his eyes light up: the abundant greenery surrounding the building, next to the Tijuca Forest.
Born and raised in the capital of São Paulo, it's only natural that the future doctor is still surprised by the lush vegetation of Rio de Janeiro, within sight right in the classroom. His high school and undergraduate studies in São Paulo didn't offer him these fascinations. But they did provide other charms, such as his close relationship with his father, whom he considers primarily responsible for his choice of a career in Mathematics.
In the 6th grade, Passoni had the privilege of being a student of his father, who teaches mathematics. At the time, his shyness prevented him from appreciating the circumstance. The mathematician recounts that it was the strong connection to his father's profession that inspired him to pursue mathematics. "Witnessing my father's devotion to science firsthand was decisive in my professional choices," he comments.
With his interests still fragmented when he was taking the university entrance exam, young Ivan Passoni made an unusual decision for his undergraduate studies, enrolling in the Molecular Sciences course at the University of São Paulo (USP). After absorbing content from areas such as Mathematics, Physics, Chemistry, Computer Science, and Biology, the then-university student decided to specialize in Mathematics, developing a monograph on Fourier Series .
With a master's degree from the University of Warwick (England) and a doctorate from IMPA, Passoni is already envisioning his next academic step. Soon, he will spend two months at the University of Cadiz (Spain), where he will attend courses and lectures, and participate in research. Regarding more concrete plans, the IMPA student states that he is already applying for postdoctoral positions at European universities.
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