Artur Avila Cordeiro de Melo (born 29 June 1979) is a Brazilian and naturalized French mathematician working primarily in the fields of

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

s and

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result ...

. He is one of the winners of the 2014 Fields Medal, being the first Latin American and lusophone to win such an award. He has been a researcher at both the

IMPA is a recurring fictional character in Nintendo's ''The Legend of Zelda'' series. She is one of the oldest and most frequently recurring characters in the series, having appeared in six titles of ''The Legend of Zelda'' games and several spin-off ...

and the CNRS (working a half-year in each one). He has been a professor at the

University of Zurich The University of Zürich (UZH, german: Universität Zürich) is a public research university located in the city of Zürich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 f ...

since September 2018.

Biography

At the age of 16, Avila won a gold medal at the 1995

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

and received a scholarship for the

Instituto Nacional de Matemática Pura e Aplicada The Instituto Nacional de Matemática Pura e Aplicada (IMPA; en, National Institute for Pure and Applied Mathematics) is widely considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is loc ...

(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. He completed his M.S. degree in 1997. Later he enrolled in the

Federal University of Rio de Janeiro The Federal University of Rio de Janeiro or University of Brazil (UFRJ; pt, Universidade Federal do Rio de Janeiro or ') is a public research university located in the state of Rio de Janeiro, Brazil. It is the largest federal university in the ...

(UFRJ), earning his B.S in mathematics. At the age of 19, Avila began writing his doctoral thesis on the theory of

s. In 2001 he finished it and received his PhD from IMPA. That same year he moved abroad to France to do postdoctoral research. He works with one-dimensional dynamics and holomorphic functions. Since 2003 he has worked as a researcher for the

Centre National de la Recherche Scientifique The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,63 ...

(CNRS) in France, later becoming a research director in 2008. His post-doctoral supervisor was

Jean-Christophe Yoccoz Jean-Christophe Yoccoz (29 May 1957 – 3 September 2016) was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems. Biography Yoccoz attended the Lycée Louis-le-Grand, during which time he was a silv ...

Mathematical work

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 Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

Barry Simon Barry Martin Simon (born 16 April 1946) is an American mathematical physicist and was the IBM professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and no ...

Mark Kac Mark Kac ( ; Polish: ''Marek Kac''; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, " Can one hear the shape of a drum?" set off research into spectral theory, the ...

promised a reward of ten martinis to whoever solved the problem: whether or not the

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...

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. 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.

Honours and recognition

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 The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current ...

prizes, and in 2009 he won the Grand Prix Jacques Herbrand from the French Academy of Sciences. In 2017 he gave the Łojasiewicz Lecture (on the "One-frequency Schrödinger operators and the almost reducibility conjecture") at the Jagiellonian University in Kraków. He was a plenary speaker at the International Congress of Mathematicians in 2010. 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 The International Association of Mathematical Physics (IAMP) was founded in 1976 to promote research in mathematical physics. It brings together research mathematicians and theoretical physicists, including students. The association's ordinary memb ...

in 2012,

TWAS Prize This is a list of recipients of the TWAS Prize, awarded annually by The World Academy of Sciences (TWAS). Summary Agricultural Sciences Biology Chemistry Earth Sciences Engineering Sciences Mathematics Medical Sc ...

in 2013 and the Fields Medal in 2014. He was elected a foreign associate of the US National Academy of Sciences in April 2019. Avila is a member of World Minds.

Diplomas, titles and awards

* 1993: Gold medal at the Olimpíada Brasileira de Matemática, Brazil * 1994: Gold medal at the Olimpíada Brasileira de Matemática, Brazil * 1995: Gold medal at the Olimpíada Brasileira de Matemática, Brazil * 1995: Gold medal at the

, Canada * 2001: PhD Thesis (advisor Welington de Melo) * 2005: Cours Peccot at the

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France. It is located in Paris n ...

* 2006: Invited address at the ICMP * 2006: Bronze medal of the CNRS * 2006: Salem Prize * 2008: Wolff Memorial Lectures,

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

* 2008: Invited address at the

European Congress of Mathematics The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses of Mathematicians (ICM). The ECM are held every four years and are timed precisely betwe ...

* 2008:

European Mathematical Society Prize European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe ...

* 2009: Grand Prix Jacques Herbrand of the French Academy of Sciences * 2010: Porter Lectures,

Rice University William Marsh Rice University (Rice University) is a private research university in Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranked among the top universities ...

* 2010: Plenary address at the International Congress of Mathematicians * 2011: Blyth Lecture Series by the

University of Toronto The University of Toronto (UToronto or U of T) is a public university, public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park (Toronto), Queen's Park. It was founded by royal charter in 1827 ...

* 2011: Michael Brin Prize in Dynamical Systems * 2012:

Early Career Award * 2013: Prize of the Brazilian Mathematical Society * 2013:

* 2014: Bellow Lectures by the

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

* 2014: Fields Medal * 2015: TWAS-Lenovo Science Prize * 2017: Łojasiewicz Lecture by the Jagiellonian University: ''One-frequency Schrödinger operators and the almost reducibility conjecture''

Extra-academic distinctions

* 2013: Member of the

Brazilian Academy of Sciences The Brazilian Academy of Sciences ( pt, italic=yes, Academia Brasileira de Ciências or ''ABC'') is the national academy of Brazil. It is headquartered in the city of Rio de Janeiro and was founded on May 3, 1916. Publications It publishes a lar ...

* 2015: Knight of the Legion of Honor * 2019: Foreign associates of the National Academy of Sciences

References

External links

Artur Avila's page at University of Zurich
* * ; Outdated links
Artur Avila's Lattes Platform

Claymath fellow page
{{DEFAULTSORT:Avila, Artur 1979 births Living people 21st-century French mathematicians Fields Medalists International Mathematical Olympiad participants Mathematical analysts People from Rio de Janeiro (city) Members of the Brazilian Academy of Sciences Recipients of the Legion of Honour Dynamical systems theorists Instituto Nacional de Matemática Pura e Aplicada alumni Instituto Nacional de Matemática Pura e Aplicada researchers Brazilian expatriate academics French people of Brazilian descent 21st-century Brazilian mathematicians TWAS laureates Foreign associates of the National Academy of Sciences Naturalized citizens of France