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Ravenel has written two books, the first on the calculation of the stable homotopy groups of spheres and the second on the
Ravenel conjectures, colloquially known among topologists respectively as the green and orange books (though the former is no longer green, but burgundy, in its current edition).
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358:. 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
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In further work, Ravenel calculates the Morava K-theories of several spaces and proves important theorems in chromatic homotopy theory together with
Hopkins. He was also one of the founders of
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At one time it seemed as if homotopy theory was utterly without system; now it is almost proved that systematic effects predominate.
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In June 2023, Robert
Burklund, Jeremy Hahn, Ishan Levy, and Tomer Schlank announced a disproof of the last remaining conjecture.
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and Morava K-theory control many qualitative phenomena, which were understood before only in special cases. Here
Ravenel uses
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In the second paper, Ravenel expands these phenomena to a global picture of stable homotopy theory leading to the
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in 1976, where he was promoted to associate professor in 1978 and professor in 1981. From 1977 to 1979 he was a
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with a thesis on exotic characteristic classes of spherical fibrations. From 1971 to 1973 he was a
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628:; Ravenel, Douglas C. (2016). "On the nonexistence of elements of Kervaire invariant one".
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in a crucial way. All but one of the
Ravenel conjectures were proved by Ethan Devinatz,
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502:"Michael Hill, Michael Hopkins, and Douglas Ravenel receive 2022 Veblen Prize"
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327:. The authors set up the so-called chromatic spectral sequence relating this
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578:, The work of M. J. Hopkins, The selected works of J. Frank Adams, Vol. II (
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178:(born February 17, 1947) is an American mathematician known for work in
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In the first of these two papers, the authors explore the stable
598:"An Old Conjecture Falls, Making Spheres a Lot More Complicated"
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Massachusetts
Institute of Technology School of Science faculty
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Localization with respect to certain periodic homology theories
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Complex cobordism and the stable homotopy groups of spheres
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Complex cobordism and the stable homotopy groups of spheres
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and Jeff Smith not long after the article got published.
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Periodic phenomena in the Adams–Novikov spectral sequence
480:"List of Fellows of the American Mathematical Society"
436:, Academic Press 1986, 2nd edition, AMS 2003, online:
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Nilpotency and periodicity in stable homotopy theory
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Nilpotency and periodicity in stable homotopy theory
531:(1988). "Nilpotence and Stable Homotopy Theory I".
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504:. American Mathematical Society. October 28, 2021
446:, Princeton, Annals of Mathematical Studies 1992
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786:"The mathematical work of Douglas C. Ravenel"
742:Bulletin of the American Mathematical Society
700:Bulletin of the American Mathematical Society
147:A definition of exotic characteristic classes
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861:Fellows of the American Mathematical Society
226:. Since 1988 he has been a professor at the
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210:. He became an assistant professor at
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846:21st-century American mathematicians
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265:. Two of his most famous papers are
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791:Homology, Homotopy and Applications
596:Hartnett, Kevin (August 22, 2023).
240:The New York Journal of Mathematics
245:In 2012 he became a fellow of the
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891:University of Washington faculty
418:1 problem for large dimensions.
206:, and in 1974/75 he visited the
886:University of Rochester faculty
756:10.1090/s0273-0979-1994-00527-0
714:10.1090/S0273-0979-1988-15615-7
482:. American Mathematical Society
325:Adams–Novikov spectral sequence
287:American Journal of Mathematics
269:, which he wrote together with
261:Ravenel's main area of work is
251:Oswald Veblen Prize in Geometry
194:in 1972 under the direction of
88:Adams–Novikov spectral sequence
780:at the University of Rochester
586:, Cambridge, 1992, S. 525–529.
190:Ravenel received his PhD from
1:
468:Mathematics Genealogy Project
247:American Mathematical Society
784:Hopkins, Michael J. (2008).
238:, 1978, and is an editor of
208:Institute for Advanced Study
856:Columbia University faculty
654:10.4007/annals.2016.184.1.1
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851:Brandeis University alumni
805:10.4310/HHA.2008.v10.n3.a1
776:Douglas Ravenel's homepage
584:Cambridge University Press
294:homotopy groups of spheres
249:. In 2022 he received the
582:and C. B. Thomas, eds.),
364:Brown–Peterson cohomology
356:chromatic homotopy theory
281:106 (1977), 469–516) and
200:C. L. E. Moore instructor
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216:University of Washington
130:University of Washington
397:said on that occasion:
228:University of Rochester
134:University of Rochester
876:Sloan Research Fellows
464:Douglas Conner Ravenel
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289:106 (1984), 351–414).
263:stable homotopy theory
176:Douglas Conner Ravenel
16:American mathematician
631:Annals of Mathematics
534:Annals of Mathematics
387:Aldridge K. Bousfield
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347:{\displaystyle E^{2}}
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279:Annals of Mathematics
881:American topologists
728:Landweber, Peter S.
523:Devinatz, Ethan S.;
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734:by Douglas Ravenel"
692:by Douglas Ravenel"
684:Landweber, Peter S.
626:Hopkins, Michael J.
525:Hopkins, Michael J.
412:elliptic cohomology
377:. In this picture,
375:Ravenel conjectures
214:in 1973 and at the
212:Columbia University
196:Edgar H. Brown, Jr.
192:Brandeis University
164:Edgar H. Brown, Jr.
126:Columbia University
83:Ravenel conjectures
73:Brandeis University
624:Hill, Michael A.;
416:Kervaire invariant
391:Michael J. Hopkins
362:and themselves on
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180:algebraic topology
25:Douglas C. Ravenel
529:Smith, Jeffrey H.
379:complex cobordism
296:by analyzing the
275:W. Stephen Wilson
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106:Scientific career
53:February 17, 1947
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122:Institutions
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98:Veblen Prize
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831:1947 births
798:(3): 1–13.
730:"Review of
688:"Review of
576:J. F. Adams
508:November 1,
395:Frank Adams
360:Jack Morava
116:Mathematics
61:Nationality
825:Categories
609:August 22,
451:References
49:1947-02-17
645:0908.3724
580:J. P. May
686:(1988).
670:13007483
236:Helsinki
86:Work on
64:American
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563:0960945
555:1971440
486:June 9,
466:at the
220:Seattle
202:at the
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152:(1972)
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141:Thesis
112:Fields
100:(2022)
94:Awards
737:(PDF)
695:(PDF)
666:S2CID
640:arXiv
551:JSTOR
611:2023
510:2021
488:2013
366:and
273:and
257:Work
186:Life
43:Born
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