Ralph Cohen
Ralph Louis Cohen (* 1952 ) is an American mathematician who studies algebraic topology and differential topology. He is a professor at Stanford University .
life and work
Cohen graduated from the University of Michigan with a bachelor's degree and received his PhD from Brandeis University in 1978 with Edgar Henry Brown (On Odd Primary Stable Homotopy Theory). He became an assistant professor at Stanford University in 1982, where he was head of the mathematics faculty from 1992 to 1995 and Barbara Kimball Browning is professor of mathematics. From 1999 to 2009 he was director of the Mathematics Research Center at Stanford.
He was visiting professor at Princeton, Oxford, Cambridge, Paris 7 and 13 University, Lille University and Copenhagen University.
In 1985 he proved the immersion conjecture (that every smooth, compact n-manifold has an immersion into the sphere , with the number of ones in the binary expansion of n). Later he turned to applications of topology in gauge field theories (topology of associated module spaces ) and in string theory ( string topology ). He also deals with the topology of loop spaces , K-theory and homotopy theory . With Graeme Segal and John DS Jones, he proposed Floer homotopy (see Floer homology ).
In 2002 he received the Distinguished Teaching Award in Stanford. In 1995 he was one of the founders of Stanford University Math Camp (SUMaC), a summer camp for mathematically gifted high school students.
From 1982 to 1984 he was a Sloan Research Fellow and in 1984 received the Presidential Young Investigator Award. He is a fellow of the American Mathematical Society .
His doctoral students include Ulrike Tillmann and Ernesto Lupercio .
Fonts
- The Immersion Conjecture for Differentiable Manifolds, Annals of Mathematics, Volume 122, 1985, pp. 237-328.
- with JDS Jones and Graeme Segal: Floer's infinite dimensional Morse theory and homotopy theory, in: The Floer Memorial Volume, Birkhäuser Verlag, Progress in Mathematics 133, 1995, pp. 297-325.
- with Graeme Segal, Ernesto Lupercio: Holomorphic curves in loop groups and Bott periodicity, Asian Journal of Mathematics, Volume 3, 1999, pp. 801-818.
- with John DS Jones: Gauge theory and string topology, Arxiv 2013
- with Kathryn Hess, Alexander A. Voronov: String Topology and Cyclic Homology, Birkhäuser 2006
- with Gunnar Carlsson : The What, Where and Why of Mathematics. A handbook for teachers . 1991.
- with Gunnar Carlsson: Topics in Algebra . 1999.
Web links
- Homepage (English)
- Profile in Stanford (English)
References and comments
- ↑ Ralph Cohen in the Mathematics Genealogy Project (English)
| personal data | |
|---|---|
| SURNAME | Cohen, Ralph |
| ALTERNATIVE NAMES | Cohen, Ralph Louis (full name) |
| BRIEF DESCRIPTION | American mathematician |
| DATE OF BIRTH | 1952 |