The Fields Medal is given to between two and four mathematicians under the age of 40 by the International Mathematical Union once every four years “to recognize outstanding achievement for existing work and for the promise of future achievement.” It is considered one of the most prestigious mathematical awards. The 2014 winners were announced on August 12. The IMA congratulates them on their achievements.
Artur Avila has made outstanding contributions to dynamical systems, analysis, and other areas, in many cases proving decisive results that solved long-standing open problems. Since 2003, he has been researcher in the Centre National de la Recherche Scientifique and became a Directeur de recherche in 2008; he is attached to the Institut de Mathematiques de Jussieu-Paris Rive Gauche.
Manjul Bhargava’s work in number theory has had a profound influence on the field. He was awarded for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves. Bhargava was a speaker at the IMA’s first Abel Prize Conference in 2011 for John Tate, who was honored for his lasting impact on the theory of numbers. (See his talk here.) Bhargava is a professor at Princeton University.
Martin Hairier was awarded for a major breakthrough in the study of stochastic partial differential equations by creating a new theory that provides tools for attacking problems that up to now had seemed impenetrable. He was an organizer and speaker for the IMA’s Annual Program Workshop on the Theory and Applications of Stochastic PDEs, under the 2012-2013 program year on Infinite Dimensional and Stochastic Dynamical Systems and Their Applications. (See his talk here.) Hairer is a Regius Professor of Mathematics at the University of Warwick.
Maryam Mirzakhani has made striking and highly original contributions to geometry and dynamical systems. Her work on Riemann surfaces and their moduli spaces bridges several mathematical disciplines – hyperbolic geometry, complex analysis, topology, and dynamics – and influences them all in return. She is the first woman to win a Fields Medal. Mirzakhani is a professor at Stanford University.
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