Artur Avila | |
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Born | Artur Avila Cordeiro de Melo 29 June 1979 Rio de Janeiro, Brazil |
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Scientific career | |
Fields | Mathematics |
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Thesis | Bifurcações de tranformações unimodais sob os pontos de vistas topológico e métrico (2001) |
Doctoral advisor | Welington de Melo |
Artur Avila Cordeiro de Melo (born 29 June 1979) is a Brazilian mathematician working primarily in the fields of dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, [2] being the first Latin American and lusophone to win such award. He has been a researcher at both the IMPA and the CNRS (working a half-year in each one). He has been a professor at the University of Zurich since September 2018.
At the age of 16, Avila won a gold medal at the 1995 International Mathematical Olympiad [3] and received a scholarship for the Instituto Nacional de Matemática Pura e Aplicada (IMPA) to start a M.S. degree while still attending high school in Colégio de São Bento and Colégio Santo Agostinho in Rio de Janeiro. [4] He completed his M.S. degree in 1997. [5] Later he enrolled in the Federal University of Rio de Janeiro (UFRJ), earning his B.S in mathematics. [6]
At the age of 19, Avila began writing his doctoral thesis on the theory of dynamical systems. In 2001 he finished it and received his PhD from IMPA. That same year he moved abroad to France to do postdoctoral research. [7] He works with one-dimensional dynamics and holomorphic functions. [8] Since 2003 he has worked as a researcher for the Centre National de la Recherche Scientifique (CNRS) in France, later becoming a research director in 2008. His post-doctoral supervisor was Jean-Christophe Yoccoz. [9]
Much of Artur Avila's work has been in the field of dynamical systems. In March 2005, at age 26, Avila and Svetlana Jitomirskaya proved the "conjecture of the ten martinis," a problem proposed by the American mathematical physicist Barry Simon. [10] Mark Kac promised a reward of ten martinis to whoever solved the problem: whether or not the spectrum of a particular type of operator is a Cantor set, given certain conditions on its parameters. The problem had been unsolved for 25 years when Avila and Jitomirskaya answered it affirmatively. [11] [12] Later that year, Avila and Marcelo Viana proved the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller flow on the moduli space of Abelian differentials on compact Riemann surfaces are all distinct. [13] [14]
Later, as a research mathematician, he received in 2006 a CNRS Bronze Medal as well as the Salem Prize, and was a Clay Research Fellow. He became the youngest professorial fellow (directeur de recherches) at the CNRS in 2008. The same year, he was awarded one of the ten prestigious European Mathematical Society prizes, and in 2009 he won the Grand Prix Jacques Herbrand from the French Academy of Sciences. [15] In 2017 he gave the Łojasiewicz Lecture (on the "One-frequency Schrödinger operators and the almost reducibility conjecture") at the Jagiellonian University in Kraków. [16]
He was a plenary speaker at the International Congress of Mathematicians in 2010. [17] In 2011, he was awarded the Michael Brin Prize in Dynamical Systems. He received the Early Career Award from the International Association of Mathematical Physics in 2012, [18] TWAS Prize in 2013 [19] and the Fields Medal in 2014. [20]
He was elected a foreign associate of the US National Academy of Sciences in April 2019. [21]
Avila is a member of World Minds.
Jean-Christophe Yoccoz was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems. Yoccoz died on 3 September 2016 at the age of 59.
Jacob Palis Jr. is a Brazilian mathematician and professor. Palis' research interests are mainly dynamical systems and differential equations. Some themes are global stability and hyperbolicity, bifurcations, attractors and chaotic systems.
The Instituto Nacional de Matemática Pura e Aplicada is considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is located in the city of Rio de Janeiro, and was formerly known simply as Instituto de Matemática Pura e Aplicada (IMPA), whose abbreviation remains in use.
Maurício Matos Peixoto,, was a Brazilian engineer and mathematician. He pioneered the studies on structural stability, and was the author of Peixoto's theorem.
Elon Lages Lima was a Brazilian mathematician whose research concerned differential topology, algebraic topology, and differential geometry. Lima was an influential figure in the development of mathematics in Brazil.
Aron Simis is a mathematician born in Recife, Brazil in 1942. He is a full professor at the Universidade Federal de Pernambuco, Brazil, and Class A research scholarship recipient from the Brazilian Research Council. He earned his PhD from Queen's University, Canada.
The Brazilian Mathematical Olympiad is a mathematics competition held every year for students of Brazil. The participants are awarded gold, silver and bronze medals in accordance with their performance. The main purpose of this competition is to help in selecting students to represent Brazil at the International Mathematical Olympiad.
Welington Celso de Melo was a Brazilian mathematician. Known for his contributions to dynamical systems theory, he served as full professor at Instituto Nacional de Matemática Pura e Aplicada from 1980 to 2016. Melo wrote numerous papers, one being a complete description of the topological behavior of 1-dimensional real dynamical systems . He proved the global hyperbolicity of renormalization for Cr unimodal maps. He was a recipient of the 2003 TWAS Prize.
The Brazilian Mathematical Olympiad of Public Schools (OBMEP) is an annual Mathematics contest created in 2005 by the Brazilian Ministério da Ciência e Tecnologia (MCT) and Ministério da Educação (MEC), in collaboration with Instituto Nacional de Matemática Pura e Aplicada (IMPA) and Sociedade Brasileira de Matemática (SBM), to stimulate the mathematics education in Brazil. It is open to public school students from fifth grade to high school. Yearly, around 18 million students are enrolled for its first round.
Fernando Codá dos Santos Cavalcanti Marques is a Brazilian mathematician working mainly in geometry, topology, partial differential equations and Morse theory. He is a professor at Princeton University. In 2012, together with André Neves, he proved the Willmore conjecture. Since then, among proving other important conjectures, Marques and Neves greatly extended Almgren–Pitts min-max theory to prove theorems about minimal surfaces.
Marcelo Miranda Viana da Silva is a Brazilian mathematician working in dynamical systems theory. He proved the Zorich–Kontsevich conjecture together with Artur Avila.
Ricardo Mañé Ramirez was a Uruguayan mathematician, known for his contributions to dynamical systems and ergodic theory. He was a doctoral student of Jacob Palis at IMPA.
Manfredo Perdigão do Carmo was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.
Svetlana Yakovlevna Jitomirskaya is a mathematician working on dynamical systems and mathematical physics. She is a distinguished professor of mathematics at Georgia Tech and UC Irvine. She is best known for solving the ten martini problem along with mathematician Artur Avila.
Enrique Ramiro Pujals is a Brazilian mathematician known for his contributions to the understanding of dynamical systems. Since fall of 2018, he has been a professor at the Graduate Center at the City University of New York.
Carlos Gustavo Tamm de Araújo Moreira is a Brazilian mathematician working on dynamical systems, ergodic theory, number theory and combinatorics. Moreira is currently a researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA), where he goes by the nickname "Gugu". He is also a member of the Brazilian Mathematical Olympiad Commission, a fanatic fan of the Brazilian football team Flamengo and a member of the Brazilian Communist Party (PCB). In October 2016, he achieved the mark of 5000 goals scored in his amateur football career. He maintains a record of his goals to show to the incredulous.
Jorge Manuel Sotomayor Tello was a Peruvian-born Brazilian mathematician who worked on differential equations, bifurcation theory, and differential equations of classical geometry.
César Leopoldo Camacho Manco, better known as simply César Camacho, is a Peruvian-born Brazilian mathematician and former director of the IMPA. His area of research is dynamical systems theory.
Arnaldo Leite Pinto Garcia is a Brazilian mathematician working on algebraic geometry and coding theory. He is a titular researcher at the IMPA.
The Olimpíada de Matemática do Grande ABC, or OMABC is a mathematical competition for pre-collegiate Brazilian students of Grande ABC region, composed by the following cities:
Among his [Avila's] previous honors are ... the Michael Brin Prize (2011).