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Basic Sciences Professor Mikhael L. Gromov The 2002 Kyoto Prize laureate in Basic Sciences is Mikhael Leonidovich Gromov of France. His contributions, including the introduction of a metric structure for families of various geometrical objects, have led to dramatic developments in geometry and many other fields of mathematics. Gromov has pioneered entirely new disciplines in a variety of fields, including geometry and analysis, and has had a substantial impact on all the mathematical sciences. Through the application of innovative ideas and radical nontraditional mathematical methods, he has also solved a great many complicated problems in modern geometry. Gromov is one of the greatest geometers of our day, following in the footsteps of Georg Friedrich Bernard Riemann and Jules Henri Poincaré of the 19th century and Élie Joseph Cartan and Shiing-shen Chern of the 20th century. Gromov's work includes his studies of isometric imbedding and the regular homotopy theory from the 1960s to the early 1970s, and his study of Riemannian spaces from the late 1970s to the 1980s, which, in particular, established revolutionary concepts. He introduced the idea of studying a huge family of spaces that contains spaces themselves as elements. He then proposed extracting the properties of individual spaces conversely using a radical speculation -- a metric structure for the family of spaces. Nearly all such radical ideas arise and end as a dream, and, therefore, it is almost impossible to obtain practical outcomes. Gromov, however, put his bold ideas into practice, and made geometry fruitful through his unique mathematical power. Their influence has been felt in many different directions. One of the principal subjects of geometry for many years - ever since Riemann and Karl Friedrich Gauss formulated the notion of spaces - was finding the relationships between the global structure of a space and local properties of a space like curvature. Gromov's theories here provided important guidelines for dealing with this subject. For example, the pinching problem (which deals with the relationship between the range of curvatures and the global structures) had traditionally been treated only in spaces of positive curvature, such as spheres; but Gromov obtained many results by studying the spaces of negative curvature, including non-Euclidean spaces. By considering the topological limits of the manifolds within a space, he also encouraged the study of Alexandrov spaces which appear in the boundaries. Discrete groups had not been well understood up to that point. Gromov, however, applied the idea of defining a metric structure for the family to the study of discrete groups, and proved that discrete groups with polynomial growth have nilpotency. Furthermore, he proposed the concept of hyperbolic groups, which make up the majority of discrete groups, and contributed significantly to the development of combinatorial group theory and topology. He also discovered entirely new topological invariants, Gromov-Witten invariants, for symplectic manifolds. Gromov has generated and contributed to the development of an extraordinarily large number of studies. A recent one concerning Riemannian spaces with singularities, in particular, would not have advanced greatly without Gromov's influence. [ back to top ] [ back to press releases ] |
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