Der Abelpreis 2009 (mit über 1 Million Dollar der mit Abstand höchstdotierte Mathematik-Preis) geht an den französischen Mathematiker Michael Gromov für seine Beiträge zur Globalen Differenzialgeometrie, Symplektischen Geometrie, Geometrischen Gruppentheorie und Partiellen Differenzialrelationen.
Der Abelpreis
wird jährlich von der Norwegischen Akademie der Wissenschaften vergeben.
(Er gilt als eine Art Ersatz dafür, daß es keinen Nobelpreis für Mathematik gibt. Über die Gründe, warum Nobel keinen Mathematik-Nobelpreis stiftete, gibt es viele anekdotische Erklärungen, die aber nach allgemeiner Meinung alle in das Reich der Fabel gehören.)
Die Verleihung findet Ende Mai in Oslo statt.
Aus der Begründung:
zur Globalen Differenzialgeometrie:
“Among Gromov’s many important contributions to Riemannian geometry, his definition of a metric structure on the set of all Riemannian manifolds known as the Gromov-Hausdorff distance stands out. This distance organizes the set of isomorphism classes of Riemannian manifolds of all possible topological types into a single metric space, in which convergence of Riemannian manifolds makes sense allowing collapse of dimension.
A spectacular result by Gromov in this area is his proof of estimates of the Betti numbers of Riemannian manifolds solely in terms of a lower bound on the sectional curvature.”
zur Symplektischen Geometrie:
“In a path-breaking work of 1985, Mikhael Gromov made the important observation that symplectic manifolds do admit plenty of compatible almost complex structures, and that they satisfy enough of the properties of Kähler manifolds to be useful. But exchanges of the coordinates in the manifolds are not holomorphic i.e. complex differentiable.
Gromov has used the existence of almost complex structures on symplectic manifolds to develop a theory of pseudoholomorphic curves, which are special maps of Riemann surfaces into almost complex manifolds. The concept of pseudoholomorphic curves has led to a number of advancements in symplectic topology, including a class of symplectic invariants now known as Gromov-Witten invariants. These invariants play a key role in string theory.”
zur Geometrischen Gruppentheorie:
“Mikhael Gromov is among the pioneers in using geometrical methods in group theory. In the early 1980s, he introduced and developed the notion of a hyperbolic group, also known as a Gromov hyperbolic group. By definition this is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic geometry.
In a seminal paper of 1987, Gromov proposed a far ranging research program for hyperbolic groups, which has inspired an entire generation of geometric group theorists.
A special highlight amomg the results of Gromov in geometric group theory is his proof of an old conjecture according to which a finitely generated group of polynomial growth has a nilpotent subgroup of finite index. Another highlight is his contributions to the construction of non-arithmetic discrete groups of hyperbolic transformations in arbitrary dimension.”
zu Partiellen Differenzialrelationen:
“Mikhael Gromov has also made important contributions to analysis. He is known for having established a homotopy method to solve differential relations, known as the h-principle.
This work was initiated in his PhD thesis of 1969, where Gromov found an astonishing new method, by which he could generalize a number of immersion theorems for manifolds M of dimension n into manifolds N of dimensions higher than n. The image of the 2-dimensional manifold known as the Klein bottle in 3-dimensional Euclidean space is a well known example of an immersion.
It came as a complete surprise when Gromov presented his elegant ideas on immersion theory, and special cases were subsequently unfolded in works by other mathematicians.”
Nachtrag: Hier die Laudatio von V.L.Hansen.
Informationen zur Vorgeschichte des Abelpreises findet man hier. Die bisherigen Preisträger seit 2003 sind:
2003 Jean-Pierre Serre (Frankreich): Homotopietheorie, Algebraische Geometrie
2004 Michael Atiyah (GB), Isadore Singer (USA): Globale Analysis
2005 Peter Lax (USA): Partielle Differentialgleichungen
2006 Lennart Carleson (Schweden): Harmonische Analysis, Dynamische Systeme
2007 Srinivasa Varadan (Indien): Wahrscheinlichkeitstheorie
2008 Jacques Tits (Belgien), John Thompson (USA): Gruppentheorie
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