Proving the immersion conjecture in 1985 secured Ralph Louis Cohen a significant position in the study of differential topology. By establishing that every smooth, compact n-manifold can be immersed into Euclidean space of dimension 2n minus the number of ones in the binary expansion of n, he provided a definitive solution to a long-standing geometric challenge.
Academic Formation and Early Career
Born in 1952, Cohen pursued his undergraduate studies at the University of Michigan, graduating in 1973. He moved to Brandeis University for doctoral work under the supervision of Edgar H. Brown, Jr., completing his thesis, On Odd Primary Stable Homotopy Theory, in 1978. Following his doctorate, he served as an L.E. Dickson Instructor at the University of Chicago before transitioning to Stanford University in 1980. He rose through the ranks at Stanford, achieving the status of full professor in 1987.
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Throughout his tenure, Cohen has focused on algebraic and differential topology. In 1991, he collaborated with Frederick Cohen, Benjamin Mann, and R. James Milgram to characterize the algebraic topology associated with the space of rational functions. His work expanded in 1995 when he, John D. S. Jones, and Graeme Segal developed a framework for understanding the homotopy theory within Floer homology in symplectic geometry. Furthermore, since 2002, he has been a contributor to the field of string topology, an area initially introduced by Moira Chas and Dennis Sullivan.
Administrative and Educational Leadership
Beyond his research, Cohen has maintained extensive administrative responsibilities at Stanford, including serving as Chair of the Mathematics Department and Director of the Mathematics Research Center. From 2010 to 2016, he functioned as the Senior Associate Dean for the Natural Sciences. His dedication to education led him to co-found the Stanford University Math Camp in 1995. He has also authored textbooks, including handbooks for teachers written with Gunnar Carlsson, and received the Distinguished Teaching Award from Stanford in 2002.
Fast facts
- Born: 1952
- Undergraduate Degree: University of Michigan, 1973
- Ph.D.: Brandeis University, 1978
- Primary Employer: Stanford University
- Fellow of the American Mathematical Society: 2013
- Field: Algebraic and Differential Topology
- Research Contribution: Immersion Conjecture, 1985
- Citizenship: United States
Questions readers ask
What is the Immersion Conjecture?
It is a mathematical result concerning the dimension of the Euclidean space into which a smooth, compact n-manifold can be immersed, defined by the formula 2n minus the number of ones in the binary expansion of n.
What professional societies is Ralph Cohen associated with?
He is a member of the American Mathematical Society and served on its Executive Committee in 2010 and its Board of Trustees in 2016.
Achievements
- Held posts at Stanford University
- Fields: mathematics, algebraic topology and differential topology
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