Artur Avila

Artur Avila
Artur Ávila (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)
TWAS Prize (2013)
Michael Brin Prize in Dynamical Systems (2011)
EMS Prize (2008)
Salem Prize (2006)
Gold medal at the International Mathematical Olympiad (1995)
Scientific career
Fields Mathematics
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 an award. He is a researcher at both the IMPA and the CNRS (working a half-year in each one).


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 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.[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.

Honours and recognition

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]

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]

He was elected a foreign associate of the US National Academy of Sciences in April 2019.[16]

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.[17]