# Brazilian mathematician named Ramanujan Prize winner

Fernando Codá Marques (32) of Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil is the winner of the 2012 Ramanujan Prize for Young Mathematicians from Developing Countries. Marques has made several major contributions to differential geometry, solving and yielding results from numerous problems mathematicians have been working on for decades. He received the prize at an award ceremony at ICTP in Trieste, Italy, on 6 September.

*Helge Holden presents the 2012 Ramanujan Prize to Fernando Codá Marques (32), Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil. Copyright: Roberto Barnaba, ICTP Photo Archives*

The Ramanujan Prize is awarded jointly by the Abdus Salam International Centre for Theoretical Physics (ICTP), Niels Henrik Abel Memorial Fund and the International Mathematical Union. The selection committee has consisted of Ngo Bao Chau, Helge Holden, Maria José Pacifico, Vasudevan Srinivas and Lothar Göttsche (Chair).

Fernando Codá Marques' latest and perhaps most prominent work, done in collaboration with André Neves of Imperial College London, is a complete proof of the Willmore Conjecture, posted pre-publication on arXiv.org in February 2012.

The Willmore Conjecture predicts the only equilibrium state of a curved surface with one hole - like a doughnut shape - subject to forces similar to those on soap bubbles, where the only forces considered are the surface tension and the amount of air contained in the soap film. The Willmore Conjecture has deep connections to fundamental questions in general relativity - the curvature of spacetime by gravity, for example - and also cell biology and lens design. The combined work of Marques and Neves offers a final proof. While the proof has yet to be published, there is so far a consensus among mathematicians studying it that Marques-Neves have proven the conjecture successfully.

Marques has also obtained results on the Yamabe Problem, completely solved Schoen's Conjecture, and counterexamples to the Rigidity Conjecture of Min-Oo.

Another marked achievement is that he solved a problem related to measurements of positive curvature, a solution detailed in a paper ICTP mathematician Claudio Arezzo called, "beautiful." The problem was that, in three dimensions or more, it was far easier to use a metric -- a kind of measurement of a distance in space - of negative curvature rather than one positive curvature, which much more rarely exist. Marques took two different positively curved metrics and proved you could join them using a gradual path of metrics of positive curvature connecting the two units of measurement. "And that's quite amazing," said Arezzo. "The theorem itself is not surprising, but nobody had any clue on how to prove it. He really came up with a nice original idea."

ICTP created the Ramanujan Prize for young mathematicians from developing countries in 2005. The Prize is funded by the Niels Henrik Abel Memorial Fund, with support from the International Mathematical Union.

The Prize is awarded annually to a researcher from a developing country less than 45 years of age, who has conducted outstanding research in a developing country. Researchers working in any branch of the mathematical sciences are eligible. The Prize carries a cash award and travel support to visit ICTP for a meeting where the Prize winner delivers a lecture.

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"On behalf of the American Mathematical Society, it is my great pleasure to congratulate Professor Yves Meyer, recipient of the 2017 Abel Prize. Professor Meyer has been a visionary in a broad range of fields, including number theory and differential equations. His fundamental work in the theory of wavelets has transformed the world of signal processing and has led to a myriad of practical applications." -- AMS President Kenneth A. Ribet (University of California, Berkeley)

Photo: Jim Brook

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