International Congress of Mathematicians
August 13 - 21, 2014
Coex , Seoul , Korea
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This video is provided by IMU and Simons Foundation.
Artur Avila
CNRS, France & IMPA, Brazil
[Artur Avila is awarded a Fields Medal]
for his profound contributions to dynamical systems theory have
changed the face of the field, using the powerful idea of
renormalization as a unifying principle.
Avila leads and shapes the field of dynamical systems. With his collaborators, he has made essential progress in many areas, including real and complex one-dimensional dynamics, spectral theory of the one-frequency Schródinger operator, flat billiards and partially hyperbolic dynamics.
Avila’s work on real one-dimensional dynamics brought completion to the subject, with full understanding of the probabilistic point of view, accompanied by a complete renormalization theory. His work in complex dynamics led to a thorough understanding of the fractal geometry of Feigenbaum Julia sets.
In the spectral theory of one-frequency difference Schródinger operators, Avila came up with a global de- scription of the phase transitions between discrete and absolutely continuous spectra, establishing surprising stratified analyticity of the Lyapunov exponent.
In the theory of flat billiards, Avila proved several long-standing conjectures on the ergodic behavior of interval-exchange maps. He made deep advances in our understanding of the stable ergodicity of typical partially hyperbolic systems.
Avila’s collaborative approach is an inspiration for a new generation of mathematicians.
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