The ten martinis promised by Mark Kac as a reward for solving a long-standing problem in spectral theory remained unclaimed for twenty-five years until Artur Ávila and Svetlana Jitomirskaya proved the conjecture in 2005. This breakthrough established that the spectrum of a specific type of operator functions as a Cantor set, securing Ávila's status in dynamical systems research.
Academic Foundation
Born in Rio de Janeiro in 1979, Ávila demonstrated mathematical aptitude early in his education at Colégio de São Bento and Colégio Santo Agostinho. At sixteen, he secured a gold medal at the 1995 International Mathematical Olympiad, which facilitated a scholarship to the Instituto Nacional de Matemática Pura e Aplicada (IMPA). He pursued his master's degree there while finishing secondary school, graduating in 1997. He subsequently earned a bachelor’s degree from the Federal University of Rio de Janeiro and completed his doctoral thesis on dynamical systems at IMPA in 2001.
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Following his PhD, Ávila relocated to France to engage in postdoctoral research under the supervision of Jean-Christophe Yoccoz. His career is marked by a consistent oscillation between institutions, balancing commitments at the Centre National de la Recherche Scientifique (CNRS) and the IMPA. He ascended to the position of research director at the CNRS in 2008. By September 2018, he transitioned to a professorial role at the University of Zurich. His output focuses heavily on one-dimensional dynamics, holomorphic functions, and spectral theory.
Theoretical Contributions
Beyond his work on the ten martinis conjecture, Ávila collaborated with Marcelo Viana to address the Zorich–Kontsevich conjecture. They successfully proved that non-trivial Lyapunov exponents within the Teichmüller flow on the moduli space of Abelian differentials on compact Riemann surfaces are distinct. His investigative reach also extends into the mechanics of dynamical billiards and the study of one-frequency Schrödinger operators.
Distinctions and Global Recognition
Ávila’s career has garnered significant international recognition. In 2014, he became the first Latin American mathematician to receive the Fields Medal. His previous accolades include the 2006 Salem Prize, the 2008 European Mathematical Society Prize, and the 2009 Grand Prix Jacques Herbrand. He holds membership in both the Brazilian Academy of Sciences and the US National Academy of Sciences, and was named a Knight of the Legion of Honour in 2015.
Fast facts
- Born: 1979, Rio de Janeiro
- Citizenship: Brazil, France
- Fields: Analysis, Dynamical Systems, Spectral Theory
- Fields Medal: 2014
- PhD: Instituto Nacional de Matemática Pura e Aplicada, 2001
- Member: National Academy of Sciences, Brazilian Academy of Sciences
- Notable Awards: Salem Prize, EMS Prize, Michael Brin Prize
Questions readers ask
What is the significance of the ten martinis conjecture?
It is a problem in spectral theory regarding whether the spectrum of a specific operator is a Cantor set, which Ávila and Svetlana Jitomirskaya proved in 2005.
Where does Artur Ávila currently hold an academic appointment?
He has been a professor at the University of Zurich since September 2018.
Achievements
- Fields medal — 2014
- Jacques Herbrand Prize — 2009
- Knight of the Legion of Honour — 2014
- CNRS bronze medal — 2006
- Salem Prize — 2006
- Held posts at Paris Diderot University, Instituto Nacional de Matemática Pura e Aplicada and University of Zurich
- Fields: mathematical analysis, dynamical systems theory and spectral theory
