Abel Prize 2009 geometry long.pdfVIP

Riemannian geometry Gromov’s work is in the field of differential ge- ometry. Differential geometry is the branch of geometry that concerns itself with smooth curved objects like curves, surfaces or even higher-di- mensional manifolds, with various additional structures, for example a Riemannian metric. A Riemannian metric on a surface allows us to measure distances and angles on the surface. A surface equipped with a Riemannian metric is called a Riemannian surface. Notice that the usual Euclidian distance is just one of many pos- sible metrics. Think of the surface as a part of a landscape and introduce a metric that expresses the differences in walking speed in various direc- tions in a given point. In a marsh the values are low compared to on dry ground. Different values in different directions from a given point reflect variations in the ground in different directions. The distance between two points in this metric is the time taken when walking between the points. One of the fundamental concepts of a Rieman- Abel Prize 2009 Geometry - the playground of Mikhail Gromov The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2009 to Mikhail Leonidovich Gromov, IHéS, Bures-sur-Yvette, France, for his revolu- tionary contributions to geometry. The Russian-French mathematician Mikhail L. Gro- mov is one of the leading mathematicians of our time. He is known for important contri- butions in many areas of mathematics, especially geometry. Mikhail Gromov has over the past 30 years produced profoundly original, general ideas, which have resulted in new perspectives on geometry and other areas of mathematics nian surface is the Gaus- sian curvature, first stud- ied by Leonhard Euler (1707-1783) and in great- er depth by Carl Friedrich Gauss (1777-1855). A plane with the Euclidian metric has zero Gaussian curvature, while the same plane equipped with the how-difficult-to-walk-metric given above might be rather curvy