Faculty

Courses Offered (subject to change)

• MTH 162:  Calculus IIA
• MTH 443:  Algebraic topology
• MTH 549:  Topics in Algebraic Topology
• MTH 550:  Special topics in algebraic topology

Selected Publications

Books

• Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press , New York, 1986.
• Nilpotence and Periodicity in Stable Homotopy Theory, Annals of Mathematics Studies, Number 128, Princeton, 1992.
• Complex Cobordism and Stable Homotopy Groups of Spheres, Second edition, AMS Chelsea Publishing, Providence, 2004.

Conference proceedings

• Algebraic Topology, Proceedings, Seattle 1985 (with H. R. Miller), Lecture Notes in Mathematics 1286, Springer-Verlag, New York, 1987.
• Algebraic Topology, Proceedings, Arcata 1986, (with G. Carlsson, R. L. Cohen and H. R. Miller), Lecture Notes in Mathematics 1370, Springer-Verlag, New York, 1989.
• Homotopy Theory and Its Applications, A Conference on Algebraic Topology in Honor of Samuel Gitler August 9-13, 1993, Cocoyoc, Mexico (with A. Adem, and R. J. Milgram), Contemporary Mathematics 188, American Mathematical Society, 1995.
• Elliptic Cohomology Geometry, Applications, and Higher Chromatic Analogues (with H. R. Miller), London Mathematical Society Lecture Notes Series (No. 342), Cambridge University Press, 2007.

Recent Papers

• Equivariant stable homotopy theory and the Kervaire invariant (with M.~Hill and M.~Hopkins, 150 pages so far), book in preparation.
• On the 3-primary Arf-Kervaire invariant problem (with M. Hill and M. Hopkins), in preparation.
• The slice spectral sequence for RO(C p n)-graded suspensions of HZ I (with M. Hill and M. Hopkins), in preparation.
• The slice spectral sequence of Mackey functors for the C4-analog of real K-theory (with M. Hill and M. Hopkins), submitted. arXiv link.
• Quillen's work on formal group laws and complex cobordism theory, Journal of K-Theory 11 (2013), no. 3, 493–506.
• A solution to the Arf-Kervaire problem (with M. Hill and M. Hopkins), Proceedings of Gokova Geometry-Topology Conference 2010, pages 21-63.
• The Kervaire invariant one problem in algebraic topology: proof (with M. Hill and M. Hopkins), written for Current Developments in Mathematics, 2010, International Press, 2011, pages 1-43.
• The Arf-Kervaire problem in algebraic topology: an introduction (with M. Hill and M. Hopkins), Current Developments in Mathematics, 2009, International Press, 2010, pages 23-57.
• On the non-existence of elements of Kervaire invariant one (with M. Hill and M. Hopkins, 221 pages), to appear in Annals of Mathematics.
• On β-elements in the Adams-Novikov spectral sequence (with H. Nakai), Journal of Topology, 2009, 2: 295-320.