The Norwegian Academy of Science and Letters awarded Dennis Sullivan the Abel Prize in Mathematics, the highest award in the field, comparable to the Nobel Prize. The north American mathematician is one of the world’s leading experts in the development of the Theory of Renormalization in Dynamic Systems. INESC TEC researcher Alberto Adrego Pinto had the opportunity to collaborate with Dennis Sullivan in the 1990s. This collaboration led to scientific work with great impact on the researcher’s career.
Alberto Adrego Pinto, INESC TEC researcher and professor at the Department of Mathematics at the Faculty of Sciences of the University of Porto, worked with Dennis Sullivan during his postgraduate master’s and PhD at the University of Warwick, United Kingdom, under the guidance of David Rand.
The contact with the current winner of the Abel Prize in Mathematics, the visits to the Institut des Hautes Études Scientifiques, in Paris and the University of Stony Brook, in the United States of America, and his stay at the Graduate Center of the City University of New York (CUNY-GC), as a post-doc researcher in the Einstein Chair of GC-CUNY, directed by Dennis Sullivan, were crucial to the development of scientific work with great impact on the INESC TEC researcher’s career.
“Above all, concerning my time at the Graduate Center, I would like to highlight the publication of the joint paper The Circle and the Solenoid, in 2006, in which we resorted to Renormalization Theory techniques to address problems related to expansive applications of the circle, of a degree greater than or equal to 2,” recalled Alberto Adrego Pinto.
The scientific results derived from the collaboration with Dennis Sullivan include papers published in various scientific journals, namely The Annals of Mathematics, Communications in Mathematical Physics, Transactions of the American Mathematical Society and Proceedings of the American Mathematical Society.
It’s also important to highlight the book published in the series Monographs in Mathematics, by Springer, where, inspired by the work of Sullivan, Alberto Adrego Pinto, in co-authorship with David Rand and Flávio Ferreira, developed new fine structures, creating differentiable structures for pseudo-Anosov applications. “These differentiable structures allow expanding the concepts of hyperbolic dynamics to surfaces of zero curvature, recovering the duality of Mañe-Bochi-Viana,” explained the researcher, also recalling the various master’s and PhD theses focusing on this area, by his students: Flávio Ferreira, João Paulo Almeida and Sérgio Dias, the latter with the co-supervision of Mário Bessa.
The Norwegian Academy of Sciences and Letters awarded the Abel Prize in Mathematics on March 23. It is an international award that acknowledges outstanding scientific work in the field of mathematics, and highest award in the area, comparable to the Nobel Prize. This year, it was awarded to mathematician Dennis Sullivan of the State University of New York (SUNY), U.S.A. Among Sullivan’s many contributions to mathematics, one of the most important is the development of new mathematical techniques required to establish the predictions of the renormalization of the physicist M. Feigenbaum as an explanation of the phenomenon of universality in dynamic systems. These new techniques have contributed significantly to the development of the so-called Theory of Renormalization in Dynamic Systems, which separates the order of chaos – with Dennis Sullivan as one of the world’s leading experts.
The INESC TEC researcher mentioned in this news piece is associated with UP-FEUP.