# Faculty

## Doug Ravenel

*Professor of Mathematics*

PhD, Brandeis University, 1972

819 Hylan Hall

(585) 275-4415

dravenel@ur.rochester.edu

Office Hours: By appointment

### 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, 493â€“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.