Douglas Ravenel
| Douglas C. Ravenel | |
|---|---|
| Born | 1947 |
| Nationality |
 United States
|
| Fields | Mathematics |
| Institutions | University of Rochester |
| Alma mater | Brandeis University |
| Doctoral advisor | Edgar H. Brown, Jr. |
| Doctoral students | Andrew Salch |
| Known for | Ravenel Conjectures Work on Adams–Novikov spectral sequence |
Douglas Conner Ravenel (born 1947) is an American mathematician known for work in algebraic topology.
He received his Ph.D. from Brandeis University in 1972 under the direction of Edgar H. Brown, Jr. with a thesis on exotic characteristic classes of spherical fibrations. From 1971 to 1973 he was instructor at the MIT and 1974/75 he was visiting the Institute for Advanced Study. He became assistant professor at the Columbia University in 1973 and at the University of Washington in Seattle in 1976, where he became associate professor in 1978 and professor in 1981. From 1977 to 1979 he was Sloan Fellow. Since 1988 he is professor at the University of Rochester. He was invited speaker at the International Congress of Mathematicians in Helsinki, 1978, and is an editor of the New York Journal of Mathematics since 1994.
In 2012 he became a fellow of the American Mathematical Society.
Ravenel's main area of work is stable homotopy theory. Two of his most famous papers are Periodic phenomena in the Adams–Novikov spectral sequence, which he wrote together with H. R. Miller and W. S. Wilson, (Annals of Mathematics, 106 (1977), 469–516) and Localization with respect to certain periodic homology theories (Amer. J. Math., 106 (1984), 351–414).
In the first of these two papers, the authors explore the stable homotopy groups of spheres by analyzing the E2-term of the Adams–Novikov spectral sequence. The authors set up the so-called chromatic spectral sequence relating this E2-term to the cohomology of the Morava stabilizer group, which exhibits certain periodic phenomena in the Adams–Novikov spectral sequence and can be seen as the beginning of chromatic homotopy theory. Applying this, the authors compute the second line of the Adams–Novikov spectral sequence and establish the non-triviality of a certain family in the stable homotopy groups of spheres. In all of this, the authors use work by Morava and themselves on Brown–Peterson cohomology and Morava K-theory.
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