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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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369:. 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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365:-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
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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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639:; 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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513:"Michael Hill, Michael Hopkins, and Douglas Ravenel receive 2022 Veblen Prize"
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338:. The authors set up the so-called chromatic spectral sequence relating this
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589:, The work of M. J. Hopkins, The selected works of J. Frank Adams, Vol. II (
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189:(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
609:"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
491:"List of Fellows of the American Mathematical Society"
447:, 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
542:(1988). "Nilpotence and Stable Homotopy Theory I".
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515:. American Mathematical Society. October 28, 2021
457:, Princeton, Annals of Mathematical Studies 1992
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797:"The mathematical work of Douglas C. Ravenel"
753:Bulletin of the American Mathematical Society
711:Bulletin of the American Mathematical Society
158:A definition of exotic characteristic classes
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872:Fellows of the American Mathematical Society
237:. Since 1988 he has been a professor at the
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221:. He became an assistant professor at
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276:. Two of his most famous papers are
877:Institute for Advanced Study people
802:Homology, Homotopy and Applications
607:Hartnett, Kevin (August 22, 2023).
251:The New York Journal of Mathematics
256:In 2012 he became a fellow of the
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902:University of Washington faculty
429:1 problem for large dimensions.
217:, and in 1974/75 he visited the
897:University of Rochester faculty
767:10.1090/s0273-0979-1994-00527-0
725:10.1090/S0273-0979-1988-15615-7
493:. American Mathematical Society
336:Adams–Novikov spectral sequence
298:American Journal of Mathematics
280:, which he wrote together with
272:Ravenel's main area of work is
262:Oswald Veblen Prize in Geometry
205:in 1972 under the direction of
99:Adams–Novikov spectral sequence
791:at the University of Rochester
597:, Cambridge, 1992, S. 525–529.
201:Ravenel received his PhD from
1:
479:Mathematics Genealogy Project
258:American Mathematical Society
795:Hopkins, Michael J. (2008).
249:, 1978, and is an editor of
219:Institute for Advanced Study
867:Columbia University faculty
665:10.4007/annals.2016.184.1.1
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862:Brandeis University alumni
816:10.4310/HHA.2008.v10.n3.a1
787:Douglas Ravenel's homepage
595:Cambridge University Press
305:homotopy groups of spheres
260:. In 2022 he received the
593:and C. B. Thomas, eds.),
375:Brown–Peterson cohomology
367:chromatic homotopy theory
292:106 (1977), 469–516) and
211:C. L. E. Moore instructor
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227:University of Washington
141:University of Washington
408:said on that occasion:
239:University of Rochester
145:University of Rochester
887:Sloan Research Fellows
475:Douglas Conner Ravenel
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300:106 (1984), 351–414).
274:stable homotopy theory
187:Douglas Conner Ravenel
27:American mathematician
18:Douglas Conner Ravenel
642:Annals of Mathematics
545:Annals of Mathematics
398:Aldridge K. Bousfield
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358:{\displaystyle E^{2}}
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290:Annals of Mathematics
892:American topologists
739:Landweber, Peter S.
534:Devinatz, Ethan S.;
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745:by Douglas Ravenel"
703:by Douglas Ravenel"
695:Landweber, Peter S.
637:Hopkins, Michael J.
536:Hopkins, Michael J.
423:elliptic cohomology
388:. In this picture,
386:Ravenel conjectures
225:in 1973 and at the
223:Columbia University
207:Edgar H. Brown, Jr.
203:Brandeis University
175:Edgar H. Brown, Jr.
137:Columbia University
94:Ravenel conjectures
84:Brandeis University
635:Hill, Michael A.;
427:Kervaire invariant
402:Michael J. Hopkins
373:and themselves on
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191:algebraic topology
36:Douglas C. Ravenel
540:Smith, Jeffrey H.
390:complex cobordism
307:by analyzing the
286:W. Stephen Wilson
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117:Scientific career
64:February 17, 1947
16:(Redirected from
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241:. He was an
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133:Institutions
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109:Veblen Prize
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842:1947 births
809:(3): 1–13.
741:"Review of
699:"Review of
587:J. F. Adams
519:November 1,
406:Frank Adams
371:Jack Morava
127:Mathematics
72:Nationality
836:Categories
620:August 22,
462:References
60:1947-02-17
656:0908.3724
591:J. P. May
697:(1988).
681:13007483
247:Helsinki
97:Work on
75:American
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673:3505179
574:0960945
566:1971440
497:June 9,
477:at the
231:Seattle
213:at the
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163:(1972)
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152:Thesis
123:Fields
111:(2022)
105:Awards
748:(PDF)
706:(PDF)
677:S2CID
651:arXiv
562:JSTOR
622:2023
521:2021
499:2013
377:and
284:and
268:Work
197:Life
54:Born
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