Ralph Louis Cohen
Ralph Louis Cohen (born 1952) is an American mathematician, specializing in algebraic topology and differential topology.[1]
Education and career
Cohen received his bachelor's degree from the University of Michigan and his Ph.D. in 1978 from Brandeis University under Edgar Henry Brown with thesis On Odd Primary Stable Homotopy Theory.[2] At Stanford University, he became in 1982 an assistant professor, was the chair of the mathematics department from 1992 to 1995, and is now the Barbara Kimball Browning Professor for Mathematics there.[1] From 1999 to 2009 he was the director of the Mathematics Research Center in Stanford.
He was a visiting professor at Princeton, Oxford, Cambridge, Université Paris Diderot, Université Paris Nord, the University of Lille, and the University of Copenhagen.[3]
In 1985 he proved the Immersion Conjecture (that each smooth, compact n-manifold has an immersion in Euclidean space of dimension 2(n)–α(n), where α(n) is the number of ones in the binary expansion of n).[4] In 1995 Cohen, John D. S. Jones, and Graeme Segal introduced an approach for understanding the homotopy theory of Floer homology.
In 2002 Cohen received the Distinguished Teaching Award from Stanford. In 1995 he was a founder of the Stanford University Math Camp (SUMaC), a summer camp for mathematically talented high school students.
In 1982 Cohen was a Sloan Fellow. In 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw. In 1984 he received the Presidential Young Investigator Award.
His doctoral students include Ulrike Tillmann and Ernesto Lupercio.
Selected publications
- The Immersion Conjecture for Differentiable Manifolds, Annals of Mathematics, vol. 122, 1985, pp. 237–328. JSTOR 1971304
- with J. D. S. 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. doi:10.1007/978-3-0348-9217-9_13
- with Graeme Segal, Ernesto Lupercio: Holomorphic curves in loop groups and Bott periodicity, Asian Journal of Mathematics, vol. 3, 1999, pp. 801–818. doi:10.4310/SDG.2002.v7.n1.a4
- with John D. S. Jones: Gauge theory and string topology, Arxiv 2013
- with Kathryn Hess, Alexander A. Voronov: String Topology and Cyclic Homology, Birkhäuser 2006[5]
- with Gunnar Carlsson: The What, Where and Why of Mathematics. A handbook for Teachers. 1991.
- with Gunnar Carlsson: Topics in Algebra. 1999.
References
- 1 2 "Ralph L. Cohen". stanford.edu.
- ↑ Ralph Louis Cohen at the Mathematics Genealogy Project
- ↑ Ralph Cohen, School of Humanities and Sciences, Stanford University
- ↑ Cohen, Ralph L. "Immersion of manifolds". Proc Natl Acad Sci USA 79 (10): 3390–3392. PMC 346422.
- ↑ Latschev, Janko (2010). "Review: String topology and cyclic homology by Ralph L. Cohen, Kathryn Hess, and Alexander A. Voronov" (PDF). Bull. Amer. Math. Soc. (N.S.) 47 (4): 705–712.
External links
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