Algebraic Topology and Category Theory

Spring 2009

topology, category theory, and their intersection.

Postdocs and other faculty interested in these topics will also attend. Talks will be contributed by people at all levels.

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

May:

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

June:

Tues 2 ?

Thur 4 ?

Tues 9 Probably not meeting (finals)

Thur 11 Extra Topology Seminar: Thomas Noll

January:

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

February:

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

March:

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

October:

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

December:

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!

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.

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 math.uchicago.edu. The template was Jespers old site.