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{{BLP sources|date=February 2013}} | |||
{{ Infobox scientist | |||
| name = Mark Mahowald | |||
| image = <!--(filename only)--> | |||
| image_size = | |||
| caption = | |||
| birth_date = {{Birth date|1931|12|1}} | |||
| birth_place = [[Albany, Minnesota]] | |||
| death_date ={{Dda|2013|7|20|1931|12|1}} | |||
| death_place = Illinois, United States | |||
| nationality = {{flag|United States}} | |||
| fields = [[Mathematics]] | |||
| workplaces = [[Northwestern University]] | |||
| alma_mater = [[University of Minnesota]] | |||
| doctoral_advisor = [[Bernard Russell Gelbaum]] | |||
| doctoral_students = [[Michael J. Hopkins]] | |||
Martin Tangora | |||
| known_for = [[Homotopy groups of spheres]] | |||
| awards = | |||
}} | |||
'''Mark Edward Mahowald''' (December 1, 1931 – July 20, 2013) was an [[United States|American]] [[mathematician]] known for work in [[algebraic topology]].<ref>{{cite web|url=http://www.legacy.com/obituaries/chicagotribune/obituary.aspx?n=mark-edward-mahowald&pid=165996488&fhid=2074#fbLoggedOut |title=MARK EDWARD MAHOWALD Obituary: View MARK MAHOWALD's Obituary by Chicago Tribune |publisher=Legacy.com |date=2013-07-20 |accessdate=2013-07-24}}</ref> | |||
==Life== | |||
Mahowald was born in Albany, Minnesota in 1931.<ref>http://books.google.ca/books?id=allYAAAAMAAJ&q=%22Mahowald,+Mark+edward%22+1931&dq=%22Mahowald,+Mark+edward%22+1931&hl=en&sa=X&ei=ue7xUYzAL6PfiAK5qoGYDg&ved=0CDcQ6AEwAg</ref> He received his Ph.D. from [[University of Minnesota]] in 1955 under the direction of [[Bernard Russell Gelbaum]] with a thesis on ''Measure in Groups''. In the sixties, he became professor at [[Syracuse University]] and around 1963 he went to [[Northwestern University]] in Chicago. | |||
==Work== | |||
Much of Mahowald's most important works concerns the [[homotopy groups of spheres]], especially using the [[Adams spectral sequence]] at the prime 2. He is known for constructing one of the first known infinite families of elements in the stable homotopy groups of spheres by showing that the classes <math>h_1h_j</math> survive the Adams spectral sequence for <math>j\geq 3</math>. In addition, he made extensive computations of the structure of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Barratt, Tangora and Kochman. Using these computations, he could show that a manifold of [[Kervaire invariant]] 1 exists in dimension 62. | |||
In addition, he contributed to the chromatic picture of the homotopy groups of spheres: His earlier work contains much on the image of the [[J-homomorphism]] and recent work together with Goerss, Henn, Karamanov and Rezk does computations in stable homotopy localized at the [[Morava K-theory]] K(2). | |||
Besides the work on the homotopy groups of spheres and related spaces, he did important work on [[Thom spectrum|Thom spectra]]. This work was used heavily in the proof of the [[nilpotence theorem]] by Devinatz, [[Michael J. Hopkins|Hopkins]] and Smith. | |||
==Awards and honors== | |||
In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-02.</ref> | |||
==Selected publications== | |||
*M. E. Mahowald and M. C. Tangora, ''Some differentials in the Adams spectral sequence'', Topology 6 (1967) 349–369. | |||
*M. G. Barratt, M. E. Mahowald and M. C. Tangora, ''Some differentials in the Adams spectral sequence II'', Topology 9 (1970) 309–316. | |||
*S.O. Kochman and M. E. Mahowald, ''On the computation of stable stems'' in ''The Cech centennial: a Conference on Homotopy Theory, June 22–26, 1993'' | |||
* M. E. Mahowald,'' A new infinite family in <math>_2\pi_*^S</math>'', Topology 16 (1977) 249–256. | |||
*P. Goerss, H-W. Henn, H.W., M. E. Mahowald and C. Rezk, ''A resolution of the K (2)-local sphere at the prime 3'', Annals of Mathematics 162 (2005), 777–822. | |||
==References== | |||
{{reflist}} | |||
== External links == | |||
*[http://www.math.northwestern.edu/people/emeritiProfiles/mark.mahowald.html Homepage at the Northwestern University] | |||
*[http://www.math.rochester.edu/u/faculty/doug/mypapers/mahowalds-groups.pdf Miller, Ravenel about Mahowald's work on the homotopy groups of spheres, pdf file] (294 kB) | |||
{{Authority control|VIAF=110574649}} | |||
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME = Mahowald, Mark | |||
| ALTERNATIVE NAMES = | |||
| SHORT DESCRIPTION = American mathematician | |||
| DATE OF BIRTH = 1931 | |||
| PLACE OF BIRTH = | |||
| DATE OF DEATH = July 20, 2013 | |||
| PLACE OF DEATH = | |||
}} | |||
{{DEFAULTSORT:Mahowald, Mark}} | |||
[[Category:1931 births]] | |||
[[Category:American mathematicians]] | |||
[[Category:University of Minnesota alumni]] | |||
[[Category:Northwestern University faculty]] | |||
[[Category:Fellows of the American Mathematical Society]] | |||
[[Category:2013 deaths]] | |||
Revision as of 03:56, 3 November 2013
Template:BLP sources Template:Infobox scientist Mark Edward Mahowald (December 1, 1931 – July 20, 2013) was an American mathematician known for work in algebraic topology.[1]
Life
Mahowald was born in Albany, Minnesota in 1931.[2] He received his Ph.D. from University of Minnesota in 1955 under the direction of Bernard Russell Gelbaum with a thesis on Measure in Groups. In the sixties, he became professor at Syracuse University and around 1963 he went to Northwestern University in Chicago.
Work
Much of Mahowald's most important works concerns the homotopy groups of spheres, especially using the Adams spectral sequence at the prime 2. He is known for constructing one of the first known infinite families of elements in the stable homotopy groups of spheres by showing that the classes survive the Adams spectral sequence for . In addition, he made extensive computations of the structure of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Barratt, Tangora and Kochman. Using these computations, he could show that a manifold of Kervaire invariant 1 exists in dimension 62.
In addition, he contributed to the chromatic picture of the homotopy groups of spheres: His earlier work contains much on the image of the J-homomorphism and recent work together with Goerss, Henn, Karamanov and Rezk does computations in stable homotopy localized at the Morava K-theory K(2).
Besides the work on the homotopy groups of spheres and related spaces, he did important work on Thom spectra. This work was used heavily in the proof of the nilpotence theorem by Devinatz, Hopkins and Smith.
Awards and honors
In 2012 he became a fellow of the American Mathematical Society.[3]
Selected publications
- M. E. Mahowald and M. C. Tangora, Some differentials in the Adams spectral sequence, Topology 6 (1967) 349–369.
- M. G. Barratt, M. E. Mahowald and M. C. Tangora, Some differentials in the Adams spectral sequence II, Topology 9 (1970) 309–316.
- S.O. Kochman and M. E. Mahowald, On the computation of stable stems in The Cech centennial: a Conference on Homotopy Theory, June 22–26, 1993
- M. E. Mahowald, A new infinite family in , Topology 16 (1977) 249–256.
- P. Goerss, H-W. Henn, H.W., M. E. Mahowald and C. Rezk, A resolution of the K (2)-local sphere at the prime 3, Annals of Mathematics 162 (2005), 777–822.
References
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External links
- Homepage at the Northwestern University
- Miller, Ravenel about Mahowald's work on the homotopy groups of spheres, pdf file (294 kB)
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