Spring 2011 homotopy theory seminar

Schedule

All talks are in RLM 10.176 at 10 AM unless otherwise noted.

Date Speaker Title
February 1 Samuel Isaacson Formal group laws and the Lazard ring
February 8   Organizational meeting
February 21 Giovanni Franklin Complex cobordism and Quillen's theorem
February 28 Giovanni Franklin More on MU
March 1 Ernie Fontes Introduction to HKR; HKR Theorem A
March 8 Aaron Royer Lubin-Tate deformation theory and Morava E-theories
March 22 Samuel Isaacson Finite subgroups of formal groups and Theorem C
March 29 — —

References

Formal group laws and the Lazard ring

  1. Hazewinkel, Michiel. Formal groups and applications. Pure and Applied Mathematics, 78. Academic Press, Inc., New York-London, 1978.
  2. Hopkins, Michael J. Complex oriented cohomology theories and the language of stacks. Course notes available via Doug Ravenel's website. [PDF]
  3. Lazard, Michel. Lois de groupes et analyseurs. Ann. Sci. Ecole Norm. Sup. (3) 72 (1955). [NUMDAM]
  4. Lazard, Michel. Sur les groupes de Lie formels à un paramètre. Bull. Soc. Math. France 83 (1955). [NUMDAM]
  5. Ravenel, Douglas C. Complex cobordism and stable homotopy groups of spheres. Second edition. American Mathematical Society, Providence, RI, 2001. [PS]

Complex cobordism and Quillen's theorem

  1. Adams, J. F. Stable homotopy and generalised homology. Reprint of the 1974 original. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1995.
  2. Quillen, Daniel. Elementary proofs of some results of cobordism theory using Steenrod operations. Advances in Math. 7 1971 29–56 (1971). [ScienceDirect]
  3. Ravenel's “green book,” cited above

Hopkins-Kuhn-Ravenel character theory

  1. Hopkins, Michael J.; Kuhn, Nicholas J.; and Ravenel, Douglas C. Generalized group characters and complex oriented cohomology theories. J. Amer. Math. Soc. 13 (2000), no. 3. [JAMS]
  2. Hopkins, Michael J.; Kuhn, Nicholas J.; and Ravenel, Douglas C. Morava K-theories of classifying spaces and generalized characters for finite groups. Algebraic topology (San Feliu de Guíxols, 1990), 186–209, Lecture Notes in Math., 1509, Springer, Berlin, 1992. [SpringerLink]

Lubin-Tate deformation theory and Morava E-theories

  1. Lubin, Jonathan and Tate, John. Formal moduli for one-parameter formal Lie groups. Bull. Soc. Math. France 94 (1966). [NUMDAM]
  2. Rezk, Charles. Notes on the Hopkins-Miller theorem. Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997), 313–366, Contemp. Math., 220, Amer. Math. Soc., Providence, RI, 1998. [PDF]