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

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

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 operator (mathematics), operators in a variety of mathematical ...

. He is one of the winners of the 2014

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

, being the first Latin American and

lusophone The Portuguese-speaking world, also known as the Lusophone world () or the Lusophony (''Lusofonia''), comprises the countries and territories in which the Portuguese language is an official, administrative, cultural, or secondary language. This ...

to win such award. He has been a researcher at both the IMPA and the

CNRS The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

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

University of Zurich The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...

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. It is widely regarded as the most prestigious mathematical competition in the wor ...

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. 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 (, UFRJ) is a public university, public research university in Rio de Janeiro, Brazil. It is the largest federal university in the country and is one of the Brazilian centers of excellence in teaching and r ...

(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 A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

from IMPA. That same year he moved abroad to France to do postdoctoral research. He works with one-dimensional dynamics and

holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex de ...

s. Since 2003 he has worked as a researcher for the

Centre National de la Recherche Scientifique The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

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

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

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 nonr ...

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

spectrum A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...

of a particular type of operator is a

Cantor set In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and mentioned by German mathematician Georg Cantor in 1883. Throu ...

, 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. Other than that, Avila also did notable research on dynamical billiards.

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

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 curren ...

prizes, and in 2009 he won the Grand Prix Jacques Herbrand from the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

. 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 in 2012,

TWAS Prize This is a list of recipients of the TWAS Prize, awarded annually by The World Academy of Sciences (TWAS) since 1985. Summary Agricultural Sciences Biology Chemistry Earth Sciences Engineering Sciences Mathematics ...

in 2013 and the

in 2014. He was elected a foreign associate of the US

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

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 (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...

* 2006: Invited address at the ICMP * 2006: Bronze medal of the

* 2006: Salem Prize * 2008: Wolff Memorial Lectures,

Caltech The California Institute of Technology (branded as Caltech) is a private university, private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small g ...

* 2008: Invited address at the European Congress of Mathematics * 2008: European Mathematical Society Prize * 2009: Grand Prix Jacques Herbrand of the French Academy of Sciences * 2010: Porter Lectures,

Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...

* 2010: Plenary address at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

* 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 whose main campus is located on the grounds that surround Queen's Park (Toronto), Queen's Park in Toronto, Ontario, Canada. It was founded by ...

* 2011: Michael Brin Prize in Dynamical Systems * 2012: International Association of Mathematical Physics Early Career Award * 2013: Prize of the Brazilian Mathematical Society * 2013:

* 2014: Bellow Lectures by the

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

* 2014:

* 2015: TWAS-Lenovo Science Prize * 2017: Łojasiewicz Lecture by the

Jagiellonian University The Jagiellonian University (, UJ) is a public research university in Kraków, Poland. Founded in 1364 by Casimir III the Great, King Casimir III the Great, it is the oldest university in Poland and one of the List of oldest universities in con ...

: ''One-frequency Schrödinger operators and the almost reducibility conjecture''

Extra-academic distinctions

* 2013: Member of the

Brazilian Academy of Sciences Brazilian commonly refers to: * Brazil, a country * Brazilians, its people * Brazilian Portuguese, its dialect Brazilian may also refer to: * "The Brazilian", a 1986 instrumental music piece by Genesis * Brazilian Café, Baghdad, Iraq (1937) * Bra ...

* 2015: Knight of the

Legion of Honor The National Order of the Legion of Honour ( ), formerly the Imperial Order of the Legion of Honour (), is the highest and most prestigious French national order of merit, both military and civil. Currently consisting of five classes, it was ...

* 2019: Foreign associates of the

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 Academics from Rio de Janeiro (city) Members of the Brazilian Academy of Sciences Recipients of the Legion of Honour Dynamical systems theorists French systems scientists 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 Research directors of the French National Centre for Scientific Research Brazilian emigrants to France Academic staff of the University of Zurich Federal University of Rio de Janeiro alumni