Artur Avila

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Artur Avila
Artur Avila (cropped).jpg
Artur Avila Cordeiro de Melo

(1979-06-29) 29 June 1979 (age 39)
Residence Rio de Janeiro, Brazil
Paris, France
  • Brazil
  • France
Education Instituto Nacional de Matemática Pura e Aplicada (PhD and MS)
Federal University of Rio de Janeiro (BS)
Known for Dynamical systems
Spectral theory
Zorich–Kontsevich conjecture
Ten martini problem
Awards Fields Medal (2014)
Michael Brin Prize in Dynamical Systems (2011)
EMS Prize (2008)
Salem Prize (2006)
Gold medal at the International Mathematical Olympiad (1995)
Scientific career
Institutions IMPA, CNRS
Paris Diderot University (Paris 7)
Instituto Nacional de Matemática Pura e Aplicada
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 and French mathematician working primarily on dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, [2] being the first Latin American to win such award. He is a researcher at both the IMPA and the CNRS (working a half-year in each one).

Dynamical system Mathematical model which describes the time dependence of a point in a geometrical space

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.

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 of studies of linear algebra and the solutions of systems of linear equations and their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter.

Fields Medal prize for mathematicians

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



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 M.S. while still attending high school in Colégio de São Bento and Colégio Santo Agostinho in Rio de Janeiro. [4] Later he enrolled in the Federal University of Rio de Janeiro (UFRJ), earning his B.S in mathematics. [5]

International Mathematical Olympiad International contest in mathematics for pre-collegiate students

The International Mathematical Olympiad (IMO) is an annual six-problem mathematical olympiad for pre-college 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 in 1980. More than 100 countries, representing over 90% of the world's population, send teams of up to six students, plus one team leader, one deputy leader, and observers.

Instituto Nacional de Matemática Pura e Aplicada

The Instituto National de Matemática Pura e Aplicada is widely 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, hence its official abbreviation.

Colégio de São Bento

Colégio de São Bento is a Benedictine school for boys in Rio de Janeiro, Brazil with a history that dates back more than 150 years. It was founded in 1858 on the hills overlooking Rio de Janeiro's harbor and the Guanabara Bay, by the adjacent Benedictine monastery. Although the school is still run by the monastery, students who attend it may come from any denomination or religion.

At the age of 19, Avila began making 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. [6] He works with one-dimensional dynamics and holomorphic functions. [7] 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. [8]

Doctor of Philosophy Postgraduate academic degree awarded by universities in many countries

A Doctor of Philosophy is the highest university degree that is conferred after a course of study by universities in most English-speaking countries. PhDs are awarded for programs across the whole breadth of academic fields. As an earned research degree, those studying for a PhD are usually required to produce original research that expands the boundaries of knowledge, normally in the form of a thesis or dissertation, and defend their work against experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title Doctor or, in non-English-speaking countries, variants such as "Dr. phil." with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, educational, or research fields are usually addressed by this title "professionally and socially in a salutation or conversation." Alternatively, holders may use post-nominal letters such as "Ph.D.", "PhD", or "DPhil". It is, however, considered incorrect to use both the title and post-nominals at the same time.

Jean-Christophe Yoccoz French mathematician and Fields Medalist

Jean-Christophe Yoccoz was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems.

In 2005, at age 26, Avila became known amongst mathematicians for proving the "Conjecture of the ten martinis", a problem proposed in 1980 by the American mathematical physicist Barry Simon. Simon promised to pay ten martini doses to whoever explained his theory about the behavior of "Schrödinger operators", mathematical tools related to quantum physics. Artur solved the problem along with mathematician Svetlana Jitomirskaya [9] [10] and was rewarded with a few rounds of martini.

Barry Simon American mathematician

Barry Martin Simon is an American mathematical physicist and the IBM Professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics, including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics.

Svetlana Jitomirskaya American mathematician

Svetlana Yakovlevna Jitomirskaya is a Soviet-American mathematician working on dynamical systems and mathematical physics.


Four Fields medallists left to right (Artur Avila, Martin Hairer (at back), Maryam Mirzakhani, with Maryam's daughter Anahita) and Manjul Bhargava at the ICM 2014 in Seoul Four Fields medallists plus epsilon.jpg
Four Fields medallists left to right (Artur Avila, Martin Hairer (at back), Maryam Mirzakhani, with Maryam's daughter Anahita) and Manjul Bhargava at the ICM 2014 in Seoul

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  [ fr ] from the French Academy of Sciences.[ citation needed ] In 2017 he gave the Łojasiewicz Lecture (on the "One-frequency Schrödinger operators and the almost reducibility conjecture") at the Jagiellonian University in Kraków. [11]

The Salem Prize, founded by the widow of Raphael Salem, is awarded to young mathematicians judged to have done outstanding work in Salem's field of interest, primarily the theory of Fourier series. The prize is considered highly prestigious and many Fields Medalists previously received Salem prize. The prize was 5000 French Francs in 1990.

Centre national de la recherche scientifique French research organisation

The French National Center for Scientific Research is the largest governmental research organisation in France and the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 engineers and technical staff, and 7,085 contractual workers. It is headquartered in Paris and has administrative offices in Brussels, Beijing, Tokyo, Singapore, Washington, D.C., Bonn, Moscow, Tunis, Johannesburg, Santiago de Chile, Israel, and New Delhi.

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 president is Pavel Exner, Scientific Director of the Doppler Institute for Mathematical Physics and Applied Mathematics in Prague.

He was a plenary speaker at the International Congress of Mathematicians in 2010. [12] 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, [13] TWAS Prize in 2013 [14] and the Fields Medal in 2014. [15]

The Michael Brin Prize in Dynamical Systems, abbreviated as the Brin Prize, is awarded to mathematicians who have made outstanding advances in the field of dynamical systems and are within 14 years of their PhD. The prize is endowed by and named after Michael Brin, whose son Sergey Brin, is a co-founder of Google. Michael Brin is a retired mathematician at the University of Maryland and a specialist in dynamical systems.

International Association of Mathematical Physics learned society

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 members are individual researchers, although associate membership is available to organizations and companies. The IAMP is governed by an executive committee elected by the ordinary members.

Mathematical work

In 2005, together with Svetlana Jitomirskaya, he solved the ten martini problem, [10] and together with Marcelo Viana, he proved the Zorich–Kontsevich conjecture. [16]

Notes and references

  2. The Guardian
  3. Web-site of the International Mathematical Olympiad: Brazil at the 36th IMO (1995)
  4. Talarico, Bruna (16 January 2010), "Gênio da matemática carioca", O Dia Online (in Portuguese), archived from the original on 22 January 2010
  5. Moreira Salles, João (January 2010), "Artur tem um problema", Piauí (in Portuguese), archived from the original on 30 June 2015
  6. Vanessa Fajardo (12 August 2014). "Pesquisador brasileiro ganha prêmio equivalente a 'Nobel' de matemática". G1.
  7. "Artur Avila". Clay Mathematics Institute.
  8. [ ] [ en ]
  9. "Solving the Ten Martini Problem" (PDF) (in Portuguese).
  10. 1 2 Avila, Artur; Jitomirskaya, Svetlana (2005). "Solving the Ten Martini Problem". The Ten Martini Problem. Lecture Notes in Physics. 690. pp. 5–16. arXiv: math/0503363 . doi:10.1007/3-540-34273-7_2. ISBN   978-3-540-31026-6.
  11. "2017 Lecture - Institute of Mathematics of the Jagiellonian University". Retrieved 2017-06-25.
  12. "ICM Plenary and Invited Speakers since 1897". International Congress of Mathematicians.
  13. The IAMP Early Career Award
  14. "Prizes and Awards". The World Academy of Sciences. 2016.
  15. 2014 IMU Prize Winners
  16. Avila, Artur; Jitomirskaya, Svetlana (2005). "Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture". arXiv: math/0508508 .

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