View source for Douglas Ravenel

{{short description|American mathematician}}
{{use mdy dates|date=November 2021}}
{{ Infobox scientist
| name              = Douglas C. Ravenel
| image             = Douglas Ravenel.jpg
| image_size        = 
| caption           = Ravenel in 1978
| birth_date        = {{birth date and age|1947|2|17}}
| birth_place       = 
| death_date        = 
| death_place       = 
| nationality       = American
| fields            = [[Mathematics]]
| workplaces        = [[Columbia University]] <br /> [[University of Washington]] <br /> [[University of Rochester]]
| alma_mater        = [[Brandeis University]]
| thesis_title      = A definition of exotic characteristic classes
| thesis_url        = https://www.proquest.com/docview/288295942
| thesis_year       = 1972
| doctoral_advisor  = [[Edgar H. Brown|Edgar H. Brown, Jr.]]
| doctoral_students =
| known_for         = [[Ravenel conjectures]] <br> Work on [[Adams–Novikov spectral sequence]]
| awards            = [[Oswald Veblen Prize in Geometry|Veblen Prize]] (2022)
}}
'''Douglas Conner Ravenel''' (born February 17, 1947) is an American mathematician known for work in [[algebraic topology]].

==Life==
Ravenel received his PhD from [[Brandeis University]] in 1972 under the direction of [[Edgar H. Brown|Edgar H. Brown, Jr.]] with a thesis on exotic characteristic classes of spherical fibrations.<ref>{{MathGenealogy|id=12024|title=Douglas Conner Ravenel}}</ref> From 1971 to 1973 he was a [[C. L. E. Moore instructor]] at the [[Massachusetts Institute of Technology]], and in 1974/75 he visited the [[Institute for Advanced Study]]. He became an assistant professor at [[Columbia University]] in 1973 and at the [[University of Washington]] in [[Seattle]] in 1976, where he was promoted to associate professor in 1978 and professor in 1981. From 1977 to 1979 he was a [[Sloan Research Fellowship|Sloan Fellow]]. Since 1988 he has been a professor at the [[University of Rochester]]. He was an [[list of International Congresses of Mathematicians Plenary and Invited Speakers|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]].<ref>{{cite web|url=https://www.ams.org/profession/fellows-list |title=List of Fellows of the American Mathematical Society|publisher=American Mathematical Society|access-date=2013-06-09}}</ref> In 2022 he received the [[Oswald Veblen Prize in Geometry]].<ref>{{cite web|url=http://www.ams.org/news?news_id=6849 |title=Michael Hill, Michael Hopkins, and Douglas Ravenel receive 2022 Veblen Prize|date=2021-10-28|publisher=American Mathematical Society|access-date=2021-11-01}}</ref>

==Work==
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 [[Haynes Miller|Haynes R. Miller]] and [[W. Stephen Wilson]] ([[Annals of Mathematics]] 106 (1977), 469–516) and ''Localization with respect to certain periodic homology theories'' ([[American Journal of Mathematics]] 106 (1984), 351–414).

In the first of these two papers, the authors explore the stable [[homotopy groups of spheres]] by analyzing the <math>E^2</math>-term of the [[Adams–Novikov spectral sequence]]. The authors set up the so-called chromatic spectral sequence relating this <math>E^2</math>-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 [[Jack Morava]] and themselves on [[Brown–Peterson cohomology]] and [[Morava K-theory]].

In the second paper, Ravenel expands these phenomena to a global picture of stable homotopy theory leading to the [[Ravenel conjectures]]. In this picture, [[complex cobordism]] and Morava K-theory control many qualitative phenomena, which were understood before only in special cases. Here Ravenel uses [[Localization of a category|localization]] in the sense of [[Aldridge K. Bousfield]] in a crucial way. All but one of the Ravenel conjectures were proved by Ethan Devinatz, [[Michael J. Hopkins]] and Jeff Smith<ref>{{cite journal|jstor=1971440|title=Nilpotence and Stable Homotopy Theory I|journal=[[Annals of Mathematics]]|volume=128|issue=2|pages=207–241|last1=Devinatz|first1=Ethan S.|last2=Hopkins|first2=Michael J.|author2-link=Michael J. Hopkins|last3=Smith|first3=Jeffrey H.|author3-link=Jeffrey H. Smith|year=1988|doi=10.2307/1971440|mr=0960945}}</ref> not long after the article got published. [[Frank Adams]] said on that occasion:

{{quote box|align = center|At one time it seemed as if homotopy theory was utterly without system; now it is almost proved that systematic effects predominate.<ref>[[Frank Adams|J. F. Adams]], The work of M. J. Hopkins, The selected works of J. Frank Adams, Vol. II ([[J. Peter May|J. P. May]] and C. B. Thomas, eds.), [[Cambridge University Press]], Cambridge, 1992, S. 525–529.</ref>}}

In June 2023, Robert Burklund, Jeremy Hahn, Ishan Levy, and Tomer Schlank announced a disproof of the last remaining conjecture.<ref>{{Cite web |last=Hartnett |first=Kevin |date=2023-08-22 |title=An Old Conjecture Falls, Making Spheres a Lot More Complicated |url=https://www.quantamagazine.org/an-old-conjecture-falls-making-spheres-a-lot-more-complicated-20230822/ |access-date=2023-08-22 |magazine=[[Quanta Magazine]] |language=en}}</ref>

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 [[elliptic cohomology]]. In 2009, he solved together with Michael Hill and Michael Hopkins the [[Kervaire invariant]] 1 problem for large dimensions.<ref>{{cite journal| last1=Hill | first1=Michael A. | last2=Hopkins | first2=Michael J. |author2-link = Michael J. Hopkins | last3=Ravenel | first3=Douglas C. |  title=On the nonexistence of elements of Kervaire invariant one | arxiv=0908.3724 | year=2016 | journal=[[Annals of Mathematics]] | volume=184 | pages=1–262 | doi=10.4007/annals.2016.184.1.1 | issue=1|mr=3505179 | s2cid=13007483 }}</ref>

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).

==Selected works==
* [https://books.google.com/books/about/Complex_Cobordism_and_Stable_Homotopy_Gr.html?id=gnTDf9wpB9sC ''Complex cobordism and the stable homotopy groups of spheres''], Academic Press 1986,<ref>{{cite journal|last=Landweber|first= Peter S.|author-link=Peter Landweber|title=Review of ''Complex cobordism and the stable homotopy groups of spheres'' by Douglas Ravenel|journal=[[Bulletin of the American Mathematical Society]] |series=New Series|volume=18|issue=1|year=1988|pages=88–91|doi=10.1090/S0273-0979-1988-15615-7|url=https://www.ams.org/journals/bull/1988-18-01/S0273-0979-1988-15615-7/S0273-0979-1988-15615-7.pdf|doi-access=free}}</ref> 2nd edition, AMS 2003, online:[https://web.archive.org/web/20090826150524/http://www.math.rochester.edu/u/faculty/doug/mu.html#repub]
* [https://books.google.com/books/about/Nilpotence_and_Periodicity_in_Stable_Hom.html?id=RA18_pxdPK4C ''Nilpotency and periodicity in stable homotopy theory''], Princeton, Annals of Mathematical Studies 1992<ref>{{cite journal|last=Landweber|first= Peter S.|title=Review of ''Nilpotency and periodicity in stable homotopy theory'' by Douglas Ravenel|journal=[[Bulletin of the American Mathematical Society]]|series=New Series|volume=31|issue=2|pages=243–246|url=https://www.ams.org/journals/bull/1994-31-02/S0273-0979-1994-00527-0/S0273-0979-1994-00527-0.pdf|doi=10.1090/s0273-0979-1994-00527-0|doi-access=free}}</ref>

==References==
{{reflist}}

==External links==
* {{official webpage|url=http://web.math.rochester.edu/people/faculty/doug/|name=Douglas Ravenel's homepage}} at the University of Rochester
* {{cite journal|url=https://projecteuclid.org/euclid.hha/1251832464|title=The mathematical work of Douglas C. Ravenel|journal=[[Homology, Homotopy and Applications]]|pages=1–13|volume=10|number=3|year=2008|last1=Hopkins|first=Michael J.|doi=10.4310/HHA.2008.v10.n3.a1|mr=2475614|doi-access=free}}

{{Authority control}}

{{DEFAULTSORT:Ravenel, Douglas}}
[[Category:1947 births]]
[[Category:Living people]]
[[Category:Place of birth missing (living people)]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Brandeis University alumni]]
[[Category:Columbia University faculty]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Institute for Advanced Study people]]
[[Category:Massachusetts Institute of Technology School of Science faculty]]
[[Category:Sloan Research Fellows]]
[[Category:American topologists]]
[[Category:University of Rochester faculty]]
[[Category:University of Washington faculty]]