Mark Mahowald

Mahowald was born in Albany, Minnesota in 1931.{{cite book|title=American Men & Women of Science|author=R.R. Bowker Company. Database Publishing Group| date=2009|volume=5| publisher=Thomson/Gale|isbn=9781414433059|url=https://books.google.com/books?id=allYAAAAMAAJ|access-date=2014-12-14}} He received his Ph.D. from the 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 Evanston, Illinois.

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 $h\_1h\_j$ survive the Adams spectral sequence for $j\backslash geq\; 3$. 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 Michael Barratt, Martin Tangora, and Stanley 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 Paul Goerss, Hans-Werner Henn, Nasko Karamanov, and Charles 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 Ethan Devinatz, Michael J. Hopkins, and Jeffrey Smith.

In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin.{{cite book|author=Mahowald, Mark|chapter=Toward a global understanding of π_{{math|*}}($S^n$)|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II|year=1998|pages=465–472|chapter-url=https://www.elibm.org/ft/10011702000}} In 2012 he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-02.

• Mark E. Mahowald and Martin C. Tangora, Some differentials in the Adams spectral sequence, Topology 6 (1967) 349–369. {{doi|10.1016/0040-9383(67)90023-7}} {{mr|0214072}}
• Michael G. Barratt, Mark E. Mahowald, and Martin C. Tangora, Some differentials in the Adams spectral sequence II, Topology 9 (1970) 309–316. {{doi|10.1016/0040-9383(70)90055-8}} {{mr|0266215}}
• Stanley O. Kochman and Mark E. Mahowald, [https://books.google.com/books?id=hcYaCAAAQBAJ&pg=PA299 On the computation of stable stems] in The Čech centennial: a Conference on Homotopy Theory, June 22–26, 1993, pp. 299–316. {{mr|1320997}}
• Mark E. Mahowald, A new infinite family in $\_2\backslash pi\_*^S$, Topology 16 (1977) 249–256. {{doi|10.1016/0040-9383(77)90005-2}}
• Paul Goerss, Hans-Werner Henn, Mark E. Mahowald, and Charles Rezk, A resolution of the K(2)-local sphere at the prime 3, Annals of Mathematics 162 (2005), 777–822. {{JSTOR|20159929}}
• Prasit Bhattacharya, Philip Egger and Mark E. Mahowald, On the periodic v2-self-map of A1, Algebraic and Geometric Topology 17 (2017) 657–692. doi:10.2140/agt.2017.17.657

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• {{MathGenealogy|7665}}
• [https://web.archive.org/web/20100610144520/http://www.math.northwestern.edu/people/emeritiProfiles/mark.mahowald.html Homepage at Northwestern University]
• {{cite web|url=http://www.math.rochester.edu/u/faculty/doug/mypapers/mahowalds-groups.pdf|archive-url=https://web.archive.org/web/20120308131323/http://www.math.rochester.edu/u/faculty/doug/mypapers/mahowalds-groups.pdf|url-status=dead|archive-date=2012-03-08| title= Miller, Ravenel about Mahowald's work on the homotopy groups of spheres}} (294 kB)

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Category:1931 births

Category:20th-century American mathematicians

Category:21st-century American mathematicians

Category:University of Minnesota alumni

Category:Northwestern University faculty

Category:Fellows of the American Mathematical Society

Category:2013 deaths

Category:People from Albany, Minnesota

Category:Mathematicians from Minnesota

Category:American topologists

Category:Syracuse University faculty

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