Topics seminar in algebraic topology

In the spring 2011, we ran a short seminar on the telescope conjecture, a major problem in chromatic homotopy theory.

Time: (some) Tuesdays 2-3 PM, unless otherwise noted.
Location: 241 Altgeld.

Date	Speaker	Title	Notes
March 15, 11 AM	Martin Frankland	Finite localizations and the telescope conjecture	Main reference: [6]
April 5	Martin Frankland	Equivalent statements of the conjecture	Notes from the talk
April 12	Nat Stapleton	The thick subcategory theorem
April 19, 11 AM	Charles Rezk	The Adams-Novikov spectral sequence of the telescope
April 26	Bertrand Guillou	Construction of type n complexes
May 3	Charles Rezk	The solution for n=1

Useful references

1. M. Hopkins and J. Smith, Nilpotence and stable homotopy theory II. Ann. of Math. (2) 148 (1998), no. 1, 1-49.
2. M. Hovey, Bousfield localization functors and Hopkins' chromatic splitting conjecture. The Cech centennial (Boston, MA, 1993), 225-250, Contemp. Math., 181, AMS, Providence, RI, 1995.
3. M. Hovey, v_n-elements in ring spectra and applications to bordism theory. Duke Math. J. 88 (1997), no. 2, 327-356.
4. M. Hovey, N. Strickland, Morava K-theories and localisation. Mem. Amer. Math. Soc. 139 (1999), no. 666.
5. M. Mahowald, D. Ravenel, and P. Shick, The triple loop space approach to the telescope conjecture. Homotopy methods in algebraic topology (Boulder, CO, 1999), 217-284, Contemp. Math., 271, AMS, Providence, RI, 2001.
6. H. Miller, Finite localizations. Papers in honor of José Adem. Bol. Soc. Mat. Mexicana (2) 37 (1992), no. 1-2, 383-389.
7. D. Ravenel, Localization with respect to certain periodic homology theories. Amer. J. Math. 106 (1984), no. 2, 351-414.
8. D. Ravenel, Life after the telescope conjecture. Algebraic K-theory and algebraic topology (Lake Louise, AB, 1991), 205-222, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 407, Kluwer Acad. Publ., Dordrecht, 1993.
9. D. Ravenel, Nilpotence and periodicity in stable homotopy theory, Ann. of Math. Stud., 128, Princeton Univ. Press, Princeton, NJ, 1992.