Ralph Louis Cohen
Ralph Louis Cohen (born 1952) is an American mathematician who works in algebraic and differential topology. He earned his bachelor’s degree from the University of Michigan in 1973 and his Ph.D. from Brandeis University in 1978, under Edgar H. Brown Jr. His thesis, On Odd Primary Stable Homotopy Theory, was published in Memoirs of the American Mathematical Society. After a postdoctoral stint as an L.E. Dickson Instructor at the University of Chicago, he joined Stanford University in 1980 as an Assistant Professor, became an Associate Professor in 1983, and was promoted to Full Professor in 1987. In 2009 he was named The Barbara Kimball Browning Professor in the School of Humanities and Sciences. He served as Chair of the Mathematics Department from 1992 to 1995 and as Director of the Mathematics Research Center from 1999 to 2009. From 2010 to 2016 he was the Senior Associate Dean for the Natural Sciences in the School of Humanities and Sciences.
Cohen has been a visiting professor at Princeton University, the University of Oxford, the University of Cambridge, Paris Diderot University, Paris 13 University, the University of Lille, and the University of Copenhagen. He helped found three major math journals: Journal of Topology, Geometry & Topology, and the Communications of the American Mathematical Society. He has supervised more than 30 Ph.D. students, including Ulrike Tillmann and Ernesto Lupercio.
His key contributions include proving the Immersion Conjecture in 1985, which says that every smooth, compact n-manifold can be immersed in Euclidean space of dimension 2n minus the number of ones in the binary expansion of n. In 1991, he, with Frederick Cohen, Benjamin Mann, and R. James Milgram, described the algebraic topology of the space of rational functions, and he later contributed to the study of related moduli spaces. In 1995 Cohen, John D. S. Jones, and Graeme Segal introduced an approach to the homotopy theory underlying Floer homology in Symplectic geometry, giving rise to Floer homotopy theory. Since 2002 he has helped develop String topology, an area started by Moira Chas and Dennis Sullivan.
Cohen has also made significant contributions to mathematics education. He founded the Stanford University Math Camp (SUMaC) in 1995, received Stanford’s Distinguished Teaching Award in 2002, and became a Bass Fellow in Undergraduate Education in 2005. In the early 2000s he co-authored a middle-school math textbook series for McGraw-Hill. He was named a Sloan Research Fellow in 1982, gave an invited lecture at the International Congress of Mathematicians in Warsaw in 1983, and received the Presidential Young Investigator Award in 1984, the NSF International Award in 1988, and was elected a Fellow of the American Mathematical Society in 2012. He also served on the AMS Executive Committee in 2010 and was elected to the AMS Board of Trustees in 2016.
This page was last edited on 2 February 2026, at 13:37 (CET).