Artur Avila Ganha a Medalha Fields

Um Brasileiro jamais ganhou um Nobel. Sim é uma vergonha universal, um símbolo de nossa incompetência, do descaso com a educação. Mas um brasileiro, Artur Avila, acabou de ganhar a medalha Fields, o equivalente ao Nobel na matemática. Esse prêmio é dado a cada 4 anos e evidentemente tem mais prestígio do que o Nobel porque premia as contribuições a matemática, a rainha das ciências. Avila faz parte do grande arsenal de matemáticos brasileiros do IMPA, de Mauricio Peixoto a Welington de Melo. Parabéns!! Segue a citação prêmio listando suas contribuições seminais `a matemática: 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