Homotopy Theory Topics Seminar

Fall 2013

Topic: Localizations and completions in topology.
Time: Wednesdays 2:30 - 3:30 PM, unless otherwise noted.
Location: MC 108.

Date	Speaker	Title	References
September 18	Daniel Schäppi	Overview and motivation	D. Sullivan. Geometric topology: localization, periodicity and Galois symmetry. The 1970 MIT notes. (Chapters 1-3) D. Sullivan. Genetics of homotopy theory and the Adams conjecture. Ann. of Math. (2) 100, 1-79, 1974.
September 25	Marcy Robertson	Localization of spaces	A.K. Bousfield. The localization of spaces with respect to homology. Topology 14, 133-150, 1975.
October 2	Marcy Robertson	Localization of spaces, part 2
October 9	Mike Misamore	Localization of spectra	A.K. Bousfield. The localization of spectra with respect to homology. Topology 18, no. 4, 257-281, 1979.
October 16	No meeting today. Happy Thanksgiving.
October 23	Martin Frankland	The R-nilpotent completion	A.K. Bousfield and D.M. Kan. Homotopy limits, completions and localizations. Lecture Notes in Mathematics, Vol. 304. Springer-Verlag, 1972. (Chapters 1-2)
October 30	Martin Frankland	Relation between completion and localization	Bousfield-Kan, Chapters 4-6. C. Casacuberta and A. Frei. Localizations as idempotent approximations to completions. J. Pure Appl. Algebra 142, no. 1, 25-33, 1999.
November 6	Omar Ortiz	Rational homotopy theory via commutative dg algebras	K. Hess. Rational homotopy theory: a brief introduction. Interactions between homotopy theory and algebra, 175-202, Contemp. Math., 436, AMS, 2007. D. Sullivan. Infinitesimal computations in topology. Inst. Hautes Études Sci. Publ. Math. No. 47, 269-331, 1978. (Sections 1-8) Y. Félix, S. Halperin, J.-C. Thomas. Rational Homotopy Theory. Graduate Texts in Mathematics, 205. Springer-Verlag, 2001. (Chapters 10-12)
November 13	Enxin Wu	Rational homotopy theory via dg Lie algebras	D. Quillen. Rational homotopy theory. Ann. of Math. (2) 90, 205-295, 1969. Félix-Halperin-Thomas, Chapters 21-24.
November 20	Hugo Bacard	p-adic homotopy theory	M. Mandell. $E_{\infty}$ algebras and p-adic homotopy theory. Topology 40, no. 1, 43-94, 2001.
November 27	Mike Misamore	Morava K-theories and the chromatic tower	D. Ravenel. Nilpotence and periodicity in stable homotopy theory. Annals of Mathematics Studies, 128. Princeton University Press, 1992. (Sections 1.5 and 7.5) J. Lurie. Chromatic Homotopy Theory. Lectures 22-24 and 32.
December 4	Daniel Schäppi	The thick subcategory theorem	Ravenel's Orange Book. Section 3.4 and Chapter 5. A. Jeanneret, P. Landweber, D. Ravenel. A note on the thick subcategory theorem. Algebraic topology: new trends in localization and periodicity, 201-207, Progr. Math., 136, 1996. J. Lurie. Chromatic Homotopy Theory. Lecture 26.

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