Proseminar on
Algebraic Topology and Category Theory
Spring 2009

Time and Place: Tuesdays and Thursdays 1:30-3:00 in Eckhart Room 203. Talks will be in the fields of
topology, category theory, and their intersection.

Audience: Graduate students in their second year or higher, with an interest in algebraic topology and/or category theory.
Postdocs and other faculty interested in these topics will also attend. Talks will be contributed by people at all levels.

Email List:

Proseminar Website: This one.

Seminar Website: UC Topology Seminar

Visitors: Andrew Blumberg May 17-June 10, Mike Mandell May 10-June 10

Course Plan:

Tues 7 Justin Noel on Nilpotency in Stable Homotopy
Thur 9 Justin Noel on Nilpotency in Stable Homotopy
Tues 14 Claire Tomesch on Complete Segal Spaces
Thur 16 Tom Fiore on the Leinster-Weber Nerve Theorem and Joachim Kock's work on Trees
17, 18, 19 Graduate Student Topology Conference
Tues 21 John Lind on Goodwille Calculus
Thur 23 No Meeting
Tues 28 Mike Shulman on Topos Theory
Thur 30 Mike Shulman on Topos Theory

2, 3 Midwest Topology Seminar
Tues 5 Pretalk by José Gómez
Thur 7 Anna Marie Bohmann on Generalizing Freyd's Generating Hypothesis
Tues 12 Mike Mandell?
Thur 14 Mike Shulman Thesis Defense
Tues 19 Topological Field Theory at Northwestern
Thur 21 Topological Field Theory at Northwestern
Tues 26 Topological Field Theory at Northwestern
Thur 28 Topological Field Theory at Northwestern

Tues 2 ?
Thur 4 ?
Tues 9 Probably not meeting (finals)
Thur 11 Extra Topology Seminar: Thomas Noll

Winter 2009

Course Plan:

List of Topics

Tues 13 Peter May on Two Sided Bar Construction and the Classification of Bundles and Fibrations
Thur 15 Tom Fiore on the Homotopy Theory of n-Fold Categories
Tues 20 Tom Fiore on Homotopy Theory, Higher Categories, and Applications
Thur 22 Mike Shulman on Enriched Model Structures
Tues 27 Peter May on Classification of Bundles
Thur 29 Rina Anno on Segal Categories vs. Quasicategories

Tues 3 John Lind on Infinite Loop Space Theory of Diagram Spectra
Thur 5 Emily Riehl on Homotopy Colimits
Tues 10 John Lind
Thur 12 Emily Riehl on Enriched Homotopy Colimits
Tues 17 Vigleik Angeltveit
Thur 19 Mike Shulman on Homotopy Colimits
Tues 24 Vigleik Angeltveit
Thur 26 Tom Fiore on Cisinski Model Structures

Tues 3 Anna Marie Bohmann on an Introduction to the Adams Spectral Sequence
Thur 5 Tom Fiore on Cisinski Model Structures
Tues 10 Anna Marie Bohmann on an Introduction to the Adams Spectral Sequence
Thur 12 Claire Tomesch
Tues 17

Autumn 2008

Course Plan:

List of Topics

Thur 2 First Talk: Emily Riehl on Factorization Systems
Thur 2 Second Talk: Justin Noel on Generalized Witt Schemes
Tues 7 Peter May on Characteristic Classes [see references below on characteristic classes]
Thur 9 Mike Shulman on Enriched Categories [see references below by Kelly and Lawvere]
Tues 14 Anna Marie Bohmann on Spectral Sequences
Thur 16 Mike Shulman on Enriched Categories and Weighted Limits
Tues 21 Anna Marie Bohmann on the Cohomology of Stiefel Manifolds via Spectral Sequences
Thur 23 Mike Shulman on Generators for Categories Notes
Tues 28 John Lind on Cohomology Operations modulo 2
Thur 30 Niles Johnson on Bicategorical Morita Theory, Azumaya, Picard, and Brauer

November (subject to change):
Tues 4 John Lind on Cohomology Operations modulo 2
Thur 6 Mike Shulman on Enriched Categories
Tues 11 No meeting
Thur 13 No meeting
Tues 18 Justin Noel on K-theory
Thur 20 Mike Shulman on Cat-enriched Categories
Tues 25 Vigleik Angeltveit on Hopf Invariant One
Thur 27 Thanksgiving Break

Tues 2 Peter May on Classifying Spaces, Cohomology, Characteristic Classes
Thur 4 Rina Anno on Homotopy Categories of Model Categories
Tues 9 Emily Riehl on Quasicategories, and Claire Tomesch on Opetopic Approaches to Higher Categories, 1:00 in E203 and 3:00 in Barn (Ryerson Bridge)
Thur 11 No Meeting, Have a good break!


Cisinski, Denis-Charles. Les préfaisceaux comme modèles des types d'homotopie.
Astérisque Volume 308, Soc. Math. France (2006), xxiv+392 pages.

Fiore, Thomas M. Nerves of Algebras à la Leinster and Weber. Talk in 2009.

Fiore, Thomas M. Grothendieckian Homotopy Theory of Presheaves à la Cisinski. Talk in 2009.

Grothendieck, Alexander. Pursuing Stacks. 1983.

Jardine, J. F. Categorical homotopy theory. Homology, Homotopy Appl. 8 (2006), no. 1, 71--144.

Kono, Akira and Tamaki, Dai. Generalized cohomology. Translated from the 2002 Japanese edition by Tamaki.
Translations of Mathematical Monographs, 230. Iwanami Series in Modern Mathematics.
American Mathematical Society, Providence, RI, 2006.

Kelly, Gregory Maxwell. Basic concepts of enriched category theory. London Mathematical Society Lecture Note Series, 64.
Cambridge University Press, Cambridge-New York, 1982.

Lawvere, F. William. Metric spaces, generalized logic, and closed categories. Rend. Sem. Mat. Fis. Milano 43 (1973), 135--166 (1974).

Mac Lane, Saunders. Homology. (Die Grundlehren der Mathematischen Wissenschaften, Bd. 114.)
Springer, Berlin, 1963; Academic Press, New York, 1963.

Maltsiniotis, Georges. La théorie de l'homotopie de Grothendieck. Astérisque No. 301 (2005), vi+140 pp.

May, J. P. Stable algebraic topology, 1945--1966. History of topology, 665--723, North-Holland, Amsterdam, 1999.

May, J. P. A Concise Course in Algebraic Topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999.
[See Chapter 23 on Characteristic Classes]

May, J.P. Notes on Characteristic Classes.

May, J. P. Books Available Online.

Milnor, John W. and Stasheff, James D. Characteristic classes. Annals of Mathematics Studies, No. 76.
Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974.

Riehl, Emily. Factorization Systems.

Riehl, Emily. Homotopy (Limits and) Colimits.

Shulman, Michael. Generators and Colimit Closures.

Previous Quarters:

Fall 2004, Winter 2005, Spring 2005, Fall 2005, Winter 2006, Spring 2006, Fall 2007.

Other Seminars:

Geometric Langlands Seminar
MIT Student Topology Seminar "Babytop"
MIT Student Topology Reading Seminar "Juvitop"
MIT Topology Seminar
Michigan Student Topology Seminar

This site is maintained by Tom Fiore, fiore AT The template was Jespers old site.