John Milnor
John Willard Milnor ( born February 20, 1931 in Orange, New Jersey) is an American mathematician. He currently teaches mathematics professor at the State University of New York at Stony Brook in New York and is co-director at the city's Institute for Mathematical Sciences.
Life
Milnor studied at Princeton University, where he also received his doctorate in 1954 at Ralph Fox ( generalize about "link groups", the node groups). While still a student, he proved in 1949 the set of Fary and Milnor, which states that the curve is not a real node if the integral of the curvature along the closed curve ≤ 4π. So He solved a conjecture of 1947 by Karol Borsuk, while he was a student of Albert W. Tucker. Borsuk and independent Werner Fenchel had proven that the total curvature of a closed curve in space is always greater than or equal to 2π, with equality only holds if the curve edged a planar convex region. Borsuk then asked if there was lower limits for the curvature of knotted curves. Since student days Milnor was also friends with John Nash, with whom he began to deal with game theory and he helped in later years, to find work after his illness.
In 1960 he became professor of mathematics at Princeton and in 1962 took over the chair. In the same year he was awarded the Fields Medal at the International Congress of Mathematicians in Stockholm for his argument is that different differentiable structures exist on the 7- dimensional sphere, it is a so-called "exotic sphere ". With Michel Kervaire, he showed that there are exactly 15, with consideration of the orientation 28 Milnor also dealt with the topology of singularities in the exotic aspects also play a role (eg Milnor fibration ).
In 1961 he took first counter-examples ( in dimension 8) for so-called main conjecture ( by Heinrich Tietze ) about the uniqueness of the Triangulierbarkeit topological manifolds.
For the Rand Corporation, he also wrote reports on game theory, including 1951 "Games against nature ," which is also about quantum mechanics. Was published in 1954 with "Sum of positional games" the first study non- neutral Games combinatorial game theory.
Milnor's books on algebraic topology and differential topology (often only mimeographed ) are regarded as standard works.
In addition to his work in differential topology, he contributed significantly to the development of the K - theory. Another area of interest is the Milnor dynamics, especially the holomorphic dynamics (including the Mandelbrot set ).
He is married to the Dusa McDuff Topologin.
Among his students John N. Mather, Jonathan Sondow, Michael Spivak and Laurent Siebenmann.
Awards
For his work Milnor received, among others, the following awards and honors: