Artur Avila

Artur Avila Cordeiro de Melo (born 29 June 1979) is a Brazilian 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).

Artur Avila
Artur Ávila (cropped)
Artur Avila Cordeiro de Melo

29 June 1979 (age 39)
ResidenceRio de Janeiro, Brazil
Paris, France
  • Brazil
  • France
EducationInstituto Nacional de Matemática Pura e Aplicada (PhD and MS)
Federal University of Rio de Janeiro (BS)
Known forDynamical systems
Spectral theory
Zorich–Kontsevich conjecture
Ten martini problem
AwardsFields 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
InstitutionsIMPA, CNRS
Paris Diderot University (Paris 7)
Instituto Nacional de Matemática Pura e Aplicada
ThesisBifurcações de tranformações unimodais sob os pontos de vistas topológico e métrico (2001)
Doctoral advisorWelington de Melo


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]

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]

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.


Four Fields medallists plus epsilon
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 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.[11]

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]

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

  1. ^
  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. ^ [[1]]
  9. ^ "Solving the Ten Martini Problem" (PDF) (in Portuguese).
  10. ^ a b 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.

Further reading

External links

1979 in science

The year 1979 in science and technology involved some significant events, listed below.

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.

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 the International Mathematical Union (IMU), a meeting that takes place every four years.

The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the mathematician's "Nobel Prize" , although there are several key differences, including frequency of award, number of awards, and age limits. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013-14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics.The prize comes with a monetary award which, since 2006, has been CA$15,000. The name of the award is in honour of Canadian mathematician John Charles Fields. Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.The medal was first awarded in 1936 to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas, and it has been awarded every four years since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 2014, the Iranian mathematician Maryam Mirzakhani became the first woman Fields Medalist. In all, sixty people have been awarded the Fields Medal.

The most recent group of Fields Medalists received their awards on 1 August 2018 at the opening ceremony of the IMU International Congress, held in Rio de Janeiro, Brazil. The medal belonging to one of the four joint winners, Caucher Birkar, was stolen shortly after the event. The ICM presented Birkar with a replacement medal a few days later.

Institut de mathématiques de Jussieu – Paris Rive Gauche

The Mathematics Institute of Jussieu–Paris Rive Gauche (Institut de mathématiques de Jussieu–Paris Rive Gauche, IMJ-PRG) is a French research institute in fundamental mathematics. It is a "mixed research unit", with three parent organizations: the Centre national de la recherche scientifique, Sorbonne University, and Paris Diderot University. It is located in Paris, split between two campuses: Jussieu and Paris Rive Gauche.

It is the largest research center for fundamental mathematics in France. More than 200 permanents researchers work at the institute, around 100 PhD students, as well as emeritus professors, postdocs, invited researchers, and ATERs, and support staff.

The IMJ-PRG is the largest research unit linked to the doctoral school of mathematical sciences of Paris center (École doctorale de sciences mathématiques de Paris-Centre). It has its own journal, the Journal de l'institut de mathématiques de Jussieu, published by Cambridge University Press and covering all areas of fundamental mathematics.Each year since 2001, the institute organizes an international summer school dedicated to a hot topic in current mathematical research.

Instituto Nacional de Matemática Pura e Aplicada

The Instituto National de Matemática Pura e Aplicada (IMPA; English: 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 located in the city of Rio de Janeiro, and was formerly known simply as Instituto de Matemática Pura e Aplicada, hence its official abbreviation.

As of 2015, IMPA does research in algebra, analysis, differential geometry, partial differential equations, computer graphics, fluid dynamics, holomorphic dynamics, mathematical economics, symplectic geometry, algebraic geometry, optimization, probability theory, dynamical systems, and ergodic theory. It is aiming to expand its lines of research to include topology, number theory, combinatorics, and discrete mathematics in general and its applications.Artur Avila, a 2014 Fields Medalist, is a researcher at IMPA and received his Ph.D there. Among its researchers also are Jacob Palis, Elon Lages Lima, Maurício Peixoto, Manfredo do Carmo, Marcelo Viana, Welington de Melo, Enrique Pujals, Harold Rosenberg, Marcos Dajczer, Carlos Gustavo Moreira, Fernando Codá Marques, César Camacho, Arnaldo Garcia, Alfredo Noel Iusem, Karl-Otto Stöhr, Robert Morris, and Carolina Araujo.

Interval exchange transformation

In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals.

Jacques Herbrand Prize

The Jacques Herbrand Prize (French: Prix Jacques Herbrand) is an award given by the French Academy of Sciences to young researchers (up to 35 years) in the field of mathematics, physics, and their non-military applications.

It was created in 1996, and first awarded in 1998.

In 2001, it was renamed to Grand Prix Jacques Herbrand .

Until 2002, the prize was given each year in both fields; since 2003, it is given alternatingly.

It is endowed with 15000, later with 20000 euros, and named in honor of the French logician Jacques Herbrand (1908-1931).

List of Brazilian mathematicians

This list of Brazilian mathematicians includes the famous mathematicians from Brazil and also those who were born in other countries but later became Brazilians.

Carolina Araujo

Artur Avila, work on dynamical systems, Fields Medal winner

Manfredo do Carmo, work on differential geometry, author of popular textbooks

Walter Carnielli

Gauss Moutinho Cordeiro

Celso Costa, discovered Costa's minimal surface

Newton da Costa, logician

César Camacho

Marcos Dajczer

Francisco Antônio Dória

Djairo Guedes de Figueiredo, noted for his researches on differential equations

Leopoldo Penna Franca

Arnaldo Garcia

Fernando Q. Gouvêa, MAA's Lester R. Ford Award winner

Alfredo Noel Iusem

Yoshiharu Kohayakawa

Elon Lages Lima, topologist and geometer, teacher and author of textbooks

Artur Oscar Lopes

Ricardo Mañé

Fernando Codá Marques, work on differential geometry, co-author of the first proof of the Willmore conjecture

Carlos Matheus

Júlio César de Mello e Souza, the Malba Tahan

Welington de Melo

Raimundo Teixeira Mendes

Carlos Gustavo Moreira

Leopoldo Nachbin, introduced Nachbin's theorem and did important work on Hewitt–Nachbin spaces

Antônio Carbonari Netto

Helena J. Nussenzveig Lopes, known for her work on partial differential equations for fluid dynamics

Valeria de Paiva

Jacob Palis, work on dynamical systems, Balzan Prize winner

Maurício Peixoto, introduced Peixoto's theorem

Paulo Pinheiro

Enrique Pujals

Paulo Ribenboim

Ruy de Queiroz

Aron Simis

Imre Simon

Joaquim Gomes de Souza, pioneer in mathematical research in Brazil

Jorge Sotomayor Tello

Keti Tenenblat

Marcelo Viana

José Felipe Voloch

List of Fields Medal winners by university affiliation

The following list comprehensively shows Fields Medal winners by university affiliations since 1936 (as of 2018, 60 winners in total). This list considers Fields medalists as equal individuals, regardless of the total number of winners who received the medal each time at the quadrennial International Congress of Mathematicians (ICM). It does not include affiliations with research institutes such as IAS and MSRI in the United States, as well as IHES and CNRS in France. In this list, universities are presented in descending order starting from those affiliated with most Fields Medal winners.

The university affiliations in this list are all official academic affiliations such as degree programs and official academic employment. Non-academic affiliations such as advisory committee and administrative staff are generally excluded. The official academic affiliations fall into three categories: 1) Alumni (graduate & attendee), 2) Long-term academic Staff, and 3) Short-term academic staff. Graduates are defined as those who hold Bachelor's, Master's, Doctorate or equivalent degrees from a university, while attendees are those who formally enrolled in degree programs at a university but did not complete the programs; thus, honorary degrees, summer attendees, exchange students and auditing students are excluded. The category of "Long-term academic staff" consists of tenure/tenure-track and equivalent academic positions, while that of "Short-term academic staff" consists of lecturers (without tenure), postdoctoral researchers, visiting professors/scholars (visitors), and equivalent academic positions. At any university, the specific academic title solely determines the type of affiliation, regardless of the actual time the position was held by a medalist.

Further explanations on "visitors" under "Short-term academic staff" are now presented. 1) All informal/personal visits are excluded from the list; 2) all employment-based visiting positions, which carry teaching/research duties, are included as affiliations in the list; 3) as for award/honor-based visiting positions, this list takes a conservative view and includes the positions as affiliations only if the medalists were required to assume employment-level duty (teaching/research) or the medalists specifically classified the visiting positions as "appointment" or similar in reliable sources such as their curriculum vitae. To be specific, some award/honor-based visiting positions such as the "Shiing-Shen Chern Visiting Professorship" in UC Berkeley are awards/honors/recognition without employment-level duty; attending meetings and giving public lectures, talks or non-curricular seminars are not employment-level duties. Finally, summer visitors are generally excluded from the list unless summer work yielded significant end products such as research publications and components of Fields-winning work, since summer terms are not part of formal academic years; the same rule applies to extension schools of universities.

The number following a person's name is the year he/she received the Fields Medal; in particular, a number with asterisk (*) means the person received the award while he/she was working at the institution (including emeritus staff) containing that asterisk. A name underlined implies that this person has been listed for a same institution previously (i.e., multiple affiliations). If a person had multiple positions under one category, only the position with highest rank is considered.

This list, together with List of Nobel laureates by university affiliation and List of Turing Award laureates by university affiliation, presents the university affiliations of people who have won highest honors in fundamental academic disciplines.

List of countries by number of Fields Medalists

This article includes a list of countries by number of Fields Medal winners. That is, a list of countries ranked by their Fields Medalists.

The figures include all Fields Medals awarded up to and including 03 August 2018 by their country of birth, origin and citizenship at the time of the announcement of the award.

Michael Brin Prize in Dynamical Systems

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.The first prize was awarded in 2008, and since 2009, it has been awarded bi-annually. Artur Avila, the 2011 awardee, went on to win the Fields Medal in 2014.

Simon problems

In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems. Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was in fact the Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it. Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential.

The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984.

Stanisław Łojasiewicz

Stanisław Łojasiewicz (9 October 1926 – 14 November 2002) was a Polish mathematician.

Svetlana Jitomirskaya

Svetlana Yakovlevna Jitomirskaya (born June 4, 1966) is a Soviet-American mathematician working on dynamical systems and mathematical physics.Jitomirskaya was born in Kharkiv. Both her mother, Valentina Borok, and her father Yakov Zhitomirskii were professors of mathematics.Her undergraduate studies were at Moscow State University, where she was a student of, among others, Vladimir Arnold and Yakov Sinai. She obtained her Ph.D. from Moscow State University in 1991 under the supervision of Yakov Sinai. She joined the mathematics department at the University of California, Irvine in 1991 as a lecturer, and became an assistant professor there in 1994 and a full professor in 2000. She is best known for solving the ten martini problem along with mathematician Artur Avila.

Timeline of women in mathematics

This is a timeline of women in mathematics.

Timeline of women in mathematics in the United States

There is a long history of women in mathematics in the United States. All women mentioned here are American unless otherwise noted.

University of Toronto Department of Mathematics

The University of Toronto Department of Mathematics is an academic department at the University of Toronto. It is located at the University's main campus at the Bahen Centre for Information Technology.

The University of Toronto was ranked first in Canada for Mathematics in 2018 by the QS World University Rankings, the Times Higher Education World University Rankings, and the Maclean's University Rankings.

Ávila (surname)

Ávila or Avila (variants include de Ávila or de Avila, D'Ávila or D'Avila, Dávila and "Davila") is a Spanish or Galician surname, originally de Ávila (who comes from the city of Ávila).

It may refer to:

Rafael "Chivirico" Dávila (born 1924), Puerto Rican, Artist, singer, musician

Adolfo Dávila (born 1965), Mexican filmmaker

Alberto Davila (born c. 1960), Mexican-American boxer

Alex Avila, American baseball player Detroit Tigers

Alexandru Davila (1862-1929), Romanian dramatist, diplomat, public administrator, and memoirist, son of Carol Davila

Andrea Ávila, Argentine long and triple jumper

Artur Avila, Brazilian mathematician

Bobby Ávila, American baseball player

Bonifacio Ávila, Colombian boxer

Carlos Dávila (born 1887), Chilean statesman

Carlos Lage Dávila (born 1951), Cuban politician

Carol Davila (1828–1884), Romanian physician, physicist and general of French origin

Charles F. Avila, American electrical engineer

Desiree Davila, (b. 1983) American Olympic marathoner

Enrico Caterino Davila (born 1576), Italian historian

Eva Avila, Canadian singer

Fidel Dávila Arrondo (born 1878), Spanish army officer

Guillermo Dávila (born 1955), Venezuelan actor and singer

Gustavo Ávila, Venezuelan jockey

Héctor Ávila, Dominican Republic boxer

Joaquín Dávila, managing director of the Carlyle Group

John Avila, American bassist from Oingo Boingo

José Antonio Dávila (born 1898), Puerto Rican poet

Juan Tomás Ávila Laurel, Equatoguinean writer

Lixion Avila, American weather forecaster

Luis Davila (disambiguation), several people

Miguel R. Dávila, President of Honduras

Mónica Farro Dávila (born 1976), Uruguayan theatrical supervedette, actress and dancer

Nick Davila, American football player

Nicolás Gómez Dávila (1913–1994), Colombian political writer,

Pedrarias Dávila (Pedro Arias de Ávila) (born 1440), colonial administrator

Pedro Ortiz Dávila ("Davilita") (born 1912), Puerto Rican singer

Ricardo Ávila, Panamanian footballer

Robert R. Davila American advocate for the deaf, Assistant Secretary of Education, and President of Gallaudet University

Rodrigo Ávila, Salvadoran politician

Rudolph B. Davila, American Medal of Honor Recipient, World War II

Saint Teresa of Ávila, Roman Catholic saint, 16th Century mystic

Ulises Dávila (born 1991), Mexican association football player

Virgilio Dávila (1869–1943), Puerto Rican poet, educator, politician and businessman

Yiye Ávila (1925–2013), Puerto Rican evangelist

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