18.919: Seminar on Algebraic Topology
Monday, Wednesday, Friday, 10:00, 2-142
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.
There are two other important components of this class.
(1) I expect a "reading response" to each paper that you are not reporting on.
It is due before the lecture on the paper. The idea is for you to
capture your thoughts about the paper: what struck you most strongly, how
does it fit with other mathematics you know, what other questions does it raise
for you? I will try to respond to each of these comments.
(2) I hope each lecture is preceded by a "practice talk." This is for you
to schedule, and attend as you like. History shows this practice to be
extremely valuable. I leave it to you to organize these.
A partial list of appropriate papers can be found
here.
Participants
Howard Beck
Luis Modes
Atticus Wang
Jaedon Whyte
Dora Woodruff
Oliver Xia
Guangxi Yan
Schedule
Mon 3 Feb Organizational meeting
Fri 7 Feb Howard Beck: Borel, "La cohomologie modulo 2 ..."
Mon 10 Feb Guangxi Yan: Serre, "Cohomologie modulo 2 ..."
Wed 12 Feb Luis Modes: Thom, "Quelques proprietes ..."
Fri 14 Feb Oliver Xia: Thom, "Quelques proprietes ..."
Mon 17 Feb Jaedon Whyte: Hirzebruch, "New Topological Methods ..."
Wed 19 Feb Atticus Wang: Milnor, "On manifolds ..."
Some resources
Some of the material at the start of the course is related to the end
of 18.906, at least as I used to give it.
Here are lecture notes.
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
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
arXiv.
Haynes Miller
Department of Mathematics 2-383
Massachusetts Institute of Technology
Cambridge, MA 02139
Email: hrm@math.mit.edu
Zoom office: https://mit.zoom.us/j/6691725321
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