Norsk
Niels Henrik Abel
 The Abel Prize
 Laureate 2009
 Press Room
 Multimedia 2009

Choosing an Abel Laureate

Professor Kristian Seip, chairman of the Abel Committee, explained why Mikhail L. Gromov was awarded the Abel Prize for 2009 after the name of this year’s Abel Laureate had been announced by Øyvind Østerud, the President of the Norwegian Academy of Science and Letters.

 

Praeses, ladies and gentlemen,

The 2009 Abel Prize is awarded to Mikhail Gromov for his revolutionary contributions to geometry.

Geometry is one of the oldest fields of mathematics; it has engaged the attention of great mathematicians through the centuries, but underwent revolutionary change during the last 50 years. Mikhail Gromov has led some of the most important developments, producing profoundly original general ideas which have resulted in new perspectives on geometry and other areas of mathematics.

Riemannian geometry developed from the study of curved surfaces and their higher dimensional analogues, and has found applications for instance to the theory of general relativity. Gromov played a decisive role in the creation of modern global Riemannian geometry. His solutions of important problems in global geometry relied on new general concepts, such as convergence of Riemannian manifolds and a compactness principle, which now bear his name.

Gromov is one of the founders of the field of global symplectic geometry. Holomorphic curves were known to be an important tool in the geometry of complex manifolds. However, the environment of integrable complex structures was too rigid. In a famous paper in 1985, he extended the concept of holomorphic curves to J-holomorphic curves on symplectic manifolds. This led to the theory of Gromov-Witten invariants, which is now an extremely active subject linked to modern quantum field theory. It also led to the creation of symplectic topology and gradually penetrated and transformed many other areas of mathematics.

Gromov’s work on groups of polynomial growth introduced ideas that forever changed the way in which a discrete infinite group is viewed. He discovered the geometry of discrete groups and solved several outstanding problems. His geometrical approach rendered complicated combinatorial arguments much more natural and powerful.

Mikhail Gromov is always in pursuit of new questions and is constantly thinking of new ideas for solutions of long-standing problems. He has produced deep and original work throughout his career and remains remarkably creative. The work of Gromov will continue to be a source of inspiration for many future mathematical discoveries.