Comparing topological field theories: the string topology of a manifold, and the Floer theory of its cotangent bundle
Plática dada por Ralph Cohen (Stanford) en las Conferencias Samuel Gitler 2016 en el Centro de Investigación y de Estudios Avanzado del Instituto Politécnico Nacional (CINVESTAV) el lunes 26 de septiembre del 2016.
keynote speaker this year is Prof. Ralph Cohen from Stanford University.
Cohen received his bachelor’s degree from the University of Michigan in 1973 and his Ph.D. in 1978 from Brandeis University where he worked under the supervision of Edgar H. Brown Jr. His thesis was titled On Odd Primary Stable Homotopy Theory. He did his postdoctoral training as an L. Dickson Instructor at the University Chicago, and then became an Assistant Professor of Mathematics at Stanford University in 1980. In 1983, he became an Associate Professor and was promoted to Full Professor in 1987. Cohen is now the Barbara Kimball Browning Professor of Mathematics at Stanford. He was Chair of the Mathematics Department from 1992 to 1995, from 1999 to 2009 he was the Director of the Mathematics Research Center at Stanford, and from 2010 to 2016 was the Senior Associate Dean for the Natural Sciences in the School of Humanities and Sciences.
Cohen has been a visiting professor at Princeton, Oxford, Cambridge, Université Paris Diderot, Université Paris Nord, the University of Lille, and the University of Copenhagen.
In 1985, Cohen 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). In 1991, Cohen, together with F. Cohen, B. Mann, R.J. Milgram, gave a complete description of the algebraic topology of the space of rational functions, and in the following years he made several contributions to the study of related moduli spaces. In 1995 Cohen, John D. S. Jones, and Graeme Segal introduced an approach for understanding the homotopy theory underlying the Floer homology theory in Symplectic Geometry. Since 2002 Cohen has been one of the leading developers and contributors to the theory of String Topology, which was introduced originally by Chas and Sullivan.
In 1995, Cohen was a founder of the Stanford University Math Camp (SUMaC), a summer camp for mathematically talented high school students. In 2002 Cohen received the Distinguished Teaching Award from Stanford University, and in 2005 he became a Bass Fellow in Undergraduate Education at Stanford.
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. In 1988 he received an NSF International Award, in 2010 he served on the Executive Committee of the American Mathematics Society and in 2011 he was elected a Fellow of the American Mathematics Society.
Cohen has been an editor of many mathematics journals and text series. In particular, he was a founding editor of both the “Journal of Topology” and “Geometry and Topology”.
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