The International Congress of Mathematicians (ICM) is the largest congress in the mathematics community. It is held once every four years under the auspices of the International Mathematical Union (IMU). This year IMC 2014 is held in Seoul, Korea. The Fields Medals are awarded during the opening ceremony on the first day of the congress.
The Fields Medalists 2014 are:
1. Artur Avila
is awarded a Fields Medal for his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.
Description in a few paragraphs:
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 Schro¨dinger 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 Schro¨dinger 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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