Michael Freedman

M. Freedman (2010)

Michael Freedman (1973)

Michael Hartley Freedman (born April 21, 1951 in Los Angeles , California ) is an American mathematician who mainly works in topology and received the Fields Medal for his proof of the Poincaré conjecture in dimension 4 .

The Poincaré conjecture says that a ( ) -fold connected closed -dimensional manifold is homeomorphic (topologically equivalent) to the -dimensional sphere. For proved this in 1961 Stephen Smale . Freedman proved the case in 1982 and received the Fields Medal for it in 1986. Grigori Perelman proved the case around 2002. ${\displaystyle n-1}$ ${\displaystyle n}$ ${\displaystyle n}$ ${\displaystyle n\geq 5}$ ${\displaystyle n=4}$ ${\displaystyle n=3}$

Freedman and Robion Kirby also showed the existence of an “exotic” manifold (that is, with a different differentiable structure than the ordinary 4-dimensional Euclidean space). ${\displaystyle R^{4}}$

Freedman is the son of the writer couple Benedict and Nancy Freedman . His father was also a mathematician. Freedman studied at Princeton University and received his doctorate in 1973 with the dissertation Codimension-Two Surgery under William Browder . He then taught at the University of California, Berkeley until 1975 . He then alternated between the Institute for Advanced Study in Princeton and the University of California, San Diego (UCSD), where he became professor in 1982.

He was a Sloan , Guggenheim , and Mac Arthur fellow. In addition to the Fields Medal, he received the National Medal of Science and the Oswald Veblen Prize in 1986 and has been a member of the National Academy of Sciences in the USA since 1984 and of the American Academy of Arts and Sciences since 1985 . In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Topological views on computational complexity ) and also in Warsaw in 1983 ( The disk theorem for four-dimensional manifolds ). He is a fellow of the American Mathematical Society .

From the 1990s onwards, he dealt with mathematical physics and the mathematics of quantum computers , including using topological methods (concept of the topological quantum computer, originally by Alexei Jurjewitsch Kitajew in 1997 ), and works for Microsoft Research . He currently works at the University of California, Santa Barbara .

Freedman is a passionate mountaineer. He is married and has three sons.

literature

• The topology of four-dimensional manifolds. Journal of Differential Geometry Vol. 17, 1982, pp. 357-453.
• with Joel Hass , G. Peter Scott : Least area incompressible surfaces in 3-manifolds. Invent. Math. 71 (1983) no. 3, 609-642.
• The disk theorem for four-dimensional manifolds. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 647-663, PWN, Warsaw, 1984.
• with Zheng-Xu He, Zhenghan Wang: Möbius energy of knots and unknots. Ann. of Math. (2) 139 (1994) no. 1, 1-50.
• Michael Hartley Freedman, Frank Quinn : Topology of 4-Manifolds. Princeton Mathematical Series, Vol. 39, Princeton University Press, Princeton, NJ 1990, ISBN 0-691-08577-3 .

Web links

Commons : Michael Freedman  - Collection of images, videos and audio files

• Homepage at Microsoft Station Q, with a list of publications
• John J. O'Connor, Edmund F. Robertson :  Michael Freedman. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Michael Freedman in the Mathematics Genealogy Project (English)