Elon Lindenstrauss is being awarded the 2010 Fields Medal for his results on measure rigidity in ergodic theory, and their applications to number theory. Lindenstrauss has made far-reaching advances in ergodic theory, the study of measure preserving transformations. His work on a conjecture of Furstenberg and Margulis concerning the measure rigidity of higher rank diagonal actions in homogeneous spaces has led to striking applications. Specifically, jointly with Einsiedler and Katok, he established the conjecture under a further hypothesis of positive entropy. It has impressive applications to the classical Littlewood Conjecture in the theory of diophantine approximation. Developing these as well other powerful ergodic theoretic and arithmetical ideas, Lindenstrauss resolved the arithmetic quantum unique ergodicity conjecture of Rudnick and Sarnak in the theory of modular forms. He and his collaborators have found many other unexpected applications of these ergodic theoretic techniques in problems in classical number theory. His work is exceptionally deep and its impact goes far beyond ergodic theory.
Degree of recognitionInternational
Granting OrganizationsInternational Mathematical Union (IMU)

Awarded at event

Event titleInternational Congress of Mathematicians 2010, ICM 2010
LocationHyderabad, IndiaShow on map
Period19 Aug 2010 → 27 Aug 2010