Douglas Ravenel is an American mathematician specializing in stable homotopy theory and chromatic homotopy theory. A professor at the University of Rochester, he is best known for developing the chromatic spectral sequence and formulating the Ravenel conjectures. His contributions to algebraic topology have been widely recognized, including his 2013 appointment as a Fellow of the American Mathematical Society and receiving the Oswald Veblen Prize in Geometry.
The 1972 doctoral thesis authored by Douglas Conner Ravenel at Brandeis University centered on exotic characteristic classes of spherical fibrations. Since completing that research under the direction of Edgar H. Brown, Jr., the American mathematician has become a central figure in the specialized study of stable homotopy theory, contributing fundamental frameworks that define modern chromatic homotopy theory.
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Born in 1947 in Alexandria, United States, Douglas Ravenel followed his doctoral studies with a C. L. E. Moore instructorship at the Massachusetts Institute of Technology, held from 1971 to 1973. He subsequently secured an assistant professorship at Columbia University in 1973. His career progressed at the University of Washington in Seattle, where he joined as an assistant professor in 1976, earned promotion to associate professor in 1978, and reached the rank of professor in 1981. He transitioned to the University of Rochester in 1988, where he remains a professor.
Contributions to Stable Homotopy Theory
Ravenel’s research involves the exploration of stable homotopy groups of spheres. His 1977 publication, Periodic phenomena in the Adams–Novikov spectral sequence, coauthored with Haynes R. Miller and W. Stephen Wilson, introduced the chromatic spectral sequence. This work, which utilized Brown–Peterson cohomology and Morava K-theory, provided a method for computing the second line of the Adams–Novikov spectral sequence. In his 1984 paper, Localization with respect to certain periodic homology theories, he developed a global perspective on these phenomena, leading to the formulation of the Ravenel conjectures. While Ethan Devinatz, Michael J. Hopkins, and Jeff Smith proved all but one of these conjectures shortly after publication, a disproof of the final conjecture was announced in June 2023 by Robert Burklund, Jeremy Hahn, Ishan Levy, and Tomer Schlank.
Collaborations and Later Research
Throughout his career, Ravenel has collaborated on significant problems within algebraic topology. He worked with Michael Hill and Michael Hopkins to solve the Kervaire invariant problem for large dimensions in 2009. Additionally, he participated in the founding of elliptic cohomology and has calculated Morava K-theories for various spaces. His written output includes three books: a text on the computation of stable homotopy groups of spheres, a volume regarding the Ravenel conjectures, and a coauthored work detailing the resolution of the Kervaire invariant problem.
Fast facts
- Born: 1947, Alexandria
- Citizenship: United States
- Doctoral Institution: Brandeis University
- Field: Mathematics
- Specialization: Homotopy theory
- Awards: Fellow of the American Mathematical Society (2013)
- Oswald Veblen Prize in Geometry recipient: 2022
- Editor: The New York Journal of Mathematics (since 1994)
Questions readers ask
Which universities have employed Douglas Ravenel?
He has held faculty positions at Columbia University, the University of Washington, and the University of Rochester.
What is the primary focus of Ravenel's research?
His work centers on stable homotopy theory, specifically concerning periodic phenomena and chromatic homotopy theory.
Achievements
- Held posts at Columbia University, University of Washington and University of Rochester
- Fields: mathematics and homotopy theory
