18.919: Seminar on Algebraic Topology

Monday, Wednesday, Friday, 11:00, on Zoom

This is a literature seminar with a focus on classic papers in Algebraic Topology. Each student will give a talk on each of three papers, chosen in consultation with me, and will also read all the papers talked on in a more cursory way, and write brief reactions to them. This course will prove useful not only to students intending to pursue algebraic topology, but also to those interested in symplectic geometry, algebraic geometry, representation theory, and combinatorics.

This seminar was founded by the late Dan Kan. A good description of the underlying intent of the seminar has been given by Phil Hirschhorn:
"I think the most important function of the Kan Seminar was to push students through the transition from someone who takes courses to someone who thinks more actively about mathematics. You had to make sense of what had been done in those seminal papers, and try to explain that to other students (and to Dan, who was a very critical audience). Speaking in that seminar was a somewhat terrifying experience for most of us, which is why Dan never allowed visitors; if the speaker felt stressed and embarrassed, at least it was only in front of others going through the same thing."

The seminar is also described on OpenCourseWare.

If you are an undergraduate interested in pursuing this course, I would like to speak with you in person before the term begins, to discuss what's involved and whether this is a good choice for you.

A partial list of appropriate papers can be found here.


Deeparaj Bhat deeparaj@mit.edu
Cameron Krulewski camkru@mit.edu
Jae Hee Lee jaehelee@mit.edu
Jiakai Li jiakaili@math.harvard.edu
Junyao Peng junyaop@mit.edu
Elia Portnoy portnoy.elia@gmail.com

Tentative Schedule

Wed 2 Sep: Organizational meeting
Fri 4 Sep: no meeting
Wed 9 Sep: Cameron: Serre
Fri 11 Sep:
Mon 14 Sep:
Wed 16 Sep:
Fri 18 Sep:
Mon 21 Sep:
Wed 23 Sep:
Fri 25 Sep:
Mon 28 Sep:
Wed 30 Sep:
Fri 2 Oct:
Mon 5 Oct:
Wed 7 Oct:
Fri 9 Oct:
Wed 14 Oct:
Fri 16 Oct:
Mon 19 Oct:
Wed 21 Oct:
Fri 23 Oct:
Mon 26 Oct:
Wed 28 Oct:
Fri 30 Oct:

Some resources

Most of the papers we will read are available online, through the MIT library's VERA database. You need an MIT certificate to use it. Many journals are also available directly through MathSciNet. Here are some other sources. From VERA you can get to JSTOR, a huge archive of journal arcticles from all disciplines, or to individual journals.

For mainly German documents visit Goettinger Digitalisierungs-Zentrum and follow links to Mathematical Literature.

For much earlier work, try la bibliotheque Gallica-Math. Maybe the most useful link from there is to NUMDAM, an archive of seminars and other mathematical documents. I especially commend to you the Seminaire Henri Cartan:
Year 1950-51: Cohomologie des groupes, suite spectrale, faisceaux
Years 1953-55: Algebre d'Eilenberg-Maclane et homotopie
Year 1958-59: Invariant de Hopf et operations cohomologiques secondaires
Year 1959-60: Periodicite des groupes d'homotopie stable des groupes classiques, d'apres Bott

For more recent work, the standard preprint server is the Front for the Mathematics ArXiv, though it seems to be out of commission right now, so use https://arxiv.org instead.

Haynes Miller
2-478, 3-7569, in principle, but more realistically: