Isadore Singer

Isadore Singer Manual ( May 3, 1924 in Detroit ) is an American mathematician specializing in Analysis at the Massachusetts Institute of Technology.

Life and work

Singer studied at the University of Michigan in 1944 and made his bachelor's degree. After three years in the U.S. Army, he went to the University of Chicago, where he received his doctorate in 1950 at Irving Segal (Lie Algebras of unbounded operators ). After graduation, he was Moore Instructor at Massachusetts Institute of Technology (MIT) in 1952 and an assistant professor at the University of California, Los Angeles ( UCLA). 1954/5 he was Visiting Assistant Professor at Columbia University and 1955/56, the Institute for Advanced Study. After that, he was Assistant Professor and in 1958 Associate Professor at MIT, where he received a full professorship in 1959. From 1970, he was there, "Norbert Wiener Professor ". In 1977, he first went as a visiting professor and from 1979 as full professor at the University of California, Berkeley. In 1983 he returned to MIT.

Singer is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. In 1969 he received the Bôcher Memorial Prize, 1988 Wigner Medal and in 2000 the Leroy P. Steele Prize of the American Mathematical Society ( AMS), whose fellow he is. In 1983 he received the National Medal of Science. 1970/72, he was Vice President of the AMS. In 1974 he gave a plenary lecture at the ICM in Vancouver ( Eigenvalues ​​of the Laplacian and Invariants of Manifolds ). In 2004 he held the Gaussian lecture the DMV.

In 2004 he was honored along with Michael Francis Atiyah for the discovery and proof of the Atiyah-Singer index theorem with the Abel Prize. The works were created in 1968 and were in the 1970s in cooperation continued with Patodi ( index theorem for manifolds with boundary ).

With DBRay he developed from 1971 to 1973 the theory of analytic torsion, the invariants of Riemannian manifolds supplies, formed from the eigenvalues ​​of the Laplace operator.

Singer regularly reads for beginners semester and wrote an introduction to topology and geometry. He is also interested in the connections of modern differential geometry to theoretical physics.

He was married since 1961 with Sheila Ruff, with whom he had five children.

His doctoral include Daniel Freed, Frank W. Warner, Nancy Stanton, Linda Rothschild, Hugo Rossi, John Lott.

Writings

  • With S. Sternberg: The infinite groups of Lie and Cartan. I. The transitive groups. J. Math Analysis 15 1965 1-114.
  • H. McKean: Curvature and the eigenvalues ​​of the Laplacian. J. Differential Geometry 1 1967 no 1, 43-69.
  • M. Atiyah: The index of elliptic operators. Ann. of Math (2 ) I: 87 1968 484-530. III: 87 1968 546-604. IV: 93 1971 119-138. V: 93 1971 139-149.
  • With D. Ray: R- torsion and the Laplacian on Riemannian manifolds. Advances in Math 7, 145-210. (1971).
  • With D. Ray: Analytic torsion for complex manifolds. Ann. of Math ( 2) 98 ( 1973), 154-177.
  • M. Atiyah. V. Patodi: Spectral asymmetry and Riemannian geometry. Math Proc. Cambridge Philos. Soc. I: 77 (1975), 43-69. II: 78 (1975 ), no 3, 405-432. III: 79 (1976 ), no 1, 71-99.
  • With S. Axelrod: Chern - Simons perturbation theory. II J. Differential Geom 39 (1994 ), no 1, 173-213.
  • With J. Thorpe: Lecture notes on elementary topology and geometry, Springer 1967, Undergraduate Texts in Mathematics, 1976
Mathematical analysis C.L.E. Moore instructor German Mathematical Society Atiyah–Singer index theorem Dan Freed John Lott (mathematician) Jean-Pierre Serre Lennart Carleson Jacques Tits Mikhail Leonidovich Gromov John Tate Yakov Sinai Integrated Authority File
418235
de