Mark Mahowald

Mark Edward Mahowald (born December 1, 1931 - † July 20, 2013 ) was an American mathematician who dealt with algebraic topology, especially homotopy theory.

Career

Mahowald received his doctorate in 1955 from the University of Minnesota in Minneapolis with Bernard Gelbaum ( Measure in Groups ) and was professor at Syracuse University from the beginning of the 1960s and then (from around 1967) at Northwestern University , where he has now retired. In 1965 he became a research fellow ( Sloan Research Fellow ) of the Alfred P. Sloan Foundation .

Mahowald worked, among other things, on the homotopy groups of spheres. He constructed manifolds with Kervaire invariant 1 in dimension 30 (with his PhD student Martin Charles Tangora) and in dimension 62 (with Michael George Barratt and JDS Jones ).

In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Toward a global understanding of ${\displaystyle \pi _{*}(S^{n})}$ ). He was a fellow of the American Mathematical Society .

Michael J. Hopkins is one of his PhD students .

Fonts

• with MC Tangora: Some differentials in the Adams spectral sequence . Topology 6 (3): 349-369.
• The image of J in the EHP sequence. Ann. of Math. (2) 116 (1982) no. 1, 65-112.
• with MG Barratt, JDS Jones: Relations Amongst Toda Brackets and the Kervaire Invariant in Dimension 62 . Journal of the London Mathematical Society. 2 30 (3): 533-550.
• with Greg Arone: The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres. Invent. Math. 135 (1999) no. 3, 743-788.
• with Paul Goerss , Hans-Werner Henn , C. Rezk: A resolution of the K (2) -local sphere at the prime 3rd Ann. of Math. (2) 162 (2005), no. 2, 777-822.
• with Eric Friedlander (Editor) "Topology and Representation Theory" 1994 (Northwestern University Conference)
• with M. Barratt (editor): "Geometric Applications of Homotopy Theory" (Evanston Conference 1977), Springer 1978
• with Stewart Priddy (editor): "Algebraic Topology", AMS 1989 (International Conference Northwestern University 1988)
• with Stewart Priddy (editor): "Homotopy theory via algebraic geometry and group representations", AMS 1998 (Conference Northwestern University 1997)
• Toward a global understanding of π _* (S ⁿ ). Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 465-472

Web links

• Page at Northwestern University
• Mark Mahowald in the Mathematics Genealogy Project (English)
• Miller, Ravenel on Mahowald's work on homotopy groups of spheres, PDF file (294 kB)

Individual evidence

1. ^ Obituary for Mark Mahowald in: Chicago Tribune
2. ↑ The Kervaire invariant one problem says that there are manifolds with Kervaire invariant 1 only in dimensions 2, 6, 14, 30 and 62. Currently (2013) the only open case of this problem is dimension 126.