Proseminar on algebraic topology Winter 2006

Instructors: Daniel Biss, Jesper Grodal, Peter May, Nathalie Wahl, ...
Website: www.math.uchicago.edu/~jg/prosem.html
Time and place: Monday and Thursday 15:00-16:30 in Eckhart Room 203
Audience: Graduate students in their second year or higher, with an interest in algebraic topology.
Textbooks: We'll use various books and research articles as detailed in the course plan below.

Various practical information and course plan:

Here is a list of topics which which we started on last year. This year we'll try to take some of these topics in more depth, in modules of 2 weeks (4 talks) per topic. If you are interested in giving a talk about one of them, drop us a line.

You should sign up for the mailing list "topology" by going to http://zaphod.uchicago.edu:8080/mailman/listinfo/topology

TALKS:
Thur Jan 5: groups and homotopy theory (Andy Chermak, pretalk for group theory talk)

First module: Stacks in homotopy theory (Justin Noel)
Mon Jan 9: Stacks -- talk 1
Thur Jan 12: Talk 2
Mon Jan 16: No seminar---MLK day
Thur Jan 19: Talk 3
Mon Jan 23: No seminar---TMF day
Thur Jan 26: Talk 4

Second module: Equivariant homotopy theory and the Sullivan Conjecture (Megan Guichard)
Mon Jan 30: Talk 1
Thur Feb 2: Talk 2
Mon Feb 6: No seminar
Thur Feb 9: Talk 3
Mon Feb 13: Talk 4

Thur Feb 16: No seminar--Larry Breen in geom langlands
Mon Feb 20: Homological stability theorems (Nathalie Wahl)
Thur Feb 23: Duality in algebra and topology (Niles Johnson)
Mon Feb 27: Topics in modern homotopy theory I (Jesper Grodal)
Thur Mar 2: Topics in modern homotopy theory II (Jesper Grodal)
Mon Mar 6: Topics in modern homotopy theory III (Jesper Grodal)
Thur Mar 9: Homological stability theorems II (Nathalie Wahl)

UNSCHEDULED TALKS:
Equivariant homotopy theory (equivariant theory and diagram categories, smith theory, Atiyah segal completion thm, Segal conj, Sullivan conj, homotopy fixed point methods, transformation groups (Adem-Davis survey), classifying spaces, orbifolds and twisted K-theory, cohomology of finite, arithmetic, and S-arithmetic groups, and the relationship to Friedlander-Milnor and unstable Quillen-Lichtenbaum conjectures, finite loop spaces are manifolds)

Structured ring spectra (following outline of Arbeitsgemeinshaft, also: Morita theory survey of Schwede and duality paper of Dwyer-Greenlees-Iyengar)

Calculus of functors (going through Calculus III by Goodwillie and survey by Kuhn)

PRACTICE TALKS:
Everyone should give at least one practice talk before their real talk, and giving as well as attending practice talks is an integral part of the course. Niles Johnson (niles at math...) is in charge of arranging the time and place for the practice talks. Contact him for more information.

PREVIOUS QUARTERS:
Fall 2004 , Winter 2005 , Spring 2005 . Fall 2005 .

OTHER STUFF: For inspiration here's a link to the student topology seminar "babytop" at MIT , the student topology reading seminar "juvitop" at MIT and the Kan seminar .