04/12/04: The last class meeting on Thursday, April 15, will
be shortened because of the colloquium at 4:30 pm by Paolo Salvatore,
who will be talking on somewhat related things. Do not forget to bring
your homework, as I will be gone for Minnesota April 16!
03/31/04: The Thursday, April 8, class meeting will be in 544
Nightingale Hall. This is where we have tea before colloquia.
03/28/04: Since I will be speaking in the Algebraic Topology
seminar at MIT Monday, March 29, at 4:30 pm, the Monday lecture will
end at 3:50 pm and my office hours will be held in the morning, 11 to
noon. Everybody is welcome to go with me to my talk at MIT.
I will also be away this Thursday, April 1 (This is not a joke), and Friday, April 2, as I will be giving a colloquium at Dartmouth. The Thursday class meeting and my office hours will be canceled. I will be around Monday morning, Tuesday, and Wednesday this week. You are welcome to see me at any time.
02/26/04: I have added a problem to Problem Set 2 and reposted
it. Have a great Spring Break! Ask questions via e-mail during the
break, as the homework is due after the break.
02/22/04: Problem Set 2 (with a few problems to be added
later) is posted and due March 8, right after the Spring Break.
02/06/04: Further hints. Problem 1: You have to show that the
standard \alpha: M_1 \tensor (M_2 \tensor M_3) --> (M_1 \tensor M_2)
\tensor M_3, which just moves the parentheses over at the level of
elements is an A-module homomorphism. You will use the coassociativity
of \Delta for that. The pentagon axiom is trivial. The hexagon axiom
and the fact that \tau = P R is an A-module homomorphism follows from
the given equations between \Delta^{op}, \Delta, and R.
Problem 2: At some point you have to show that via those transpositions \tau, you may define a morphism \Sigma_m --> P(m,m). Use the fact that the symmetric group \Sigma_m is generated by transpositions \tau of two adjacent elements and the relations \tau^2 = id and \tau_{12} \tau_{23} \tau_{12} = \tau_{23} \tau_{12} \tau_{23}. Deduce the second equation from the hexagon axiom, which will become a "triangle" axiom, because \alpha = id.
02/04/04: I forgot that there might be no inputs or no
outputs, when I wrote the hint to Problem 5, so I added caps into
consideration and rewrote the hint. The corrected hint is under the
same link.
02/03/04: A hint to Problem 5 is posted here.
01/27/04: I have also changed the due date for the first
problem set to Monday, February 9. The old due date, February 7, is
Saturday.
01/27/04: I am changing my office hours to 4:30-5:30 Mondays
and 11-12 Thursdays to avoid conflicts with the
Geometry-Algebra-Singularities-Combinatorics Seminar and the Basic
Notions Seminar.
01/27/04: I have posted another version, marked January 27, of
Problem Set 1 with corrections in Problems 4 and 6. Please, make sure
to download the new version. Sorry about the confusion.
01/21/04: I have posted a new version, marked January 21, of
Problem Set 1 with minor corrections. Please, make sure to download
the new version.
01/21/04: There will be no regular course meeting Thursday,
January 23. I encourage you to attend my colloquium talk on String
Topology at 4:30 pm the same day, same room, instead. There will also
be tea there starting at 4 pm.
01/21/04: I posted half of Problem Set 1 first at the end of
the long weekend and now removed the first part and posted a complete
Problem Set in one file, having made a few corrections to the original
posting. The homework may look short, but must be time-consuming. So,
try to cooperate with the other students on solving the problems and
also consult with me, should you have any questions or get stuck.
01/16/04: I am sorry, I was not able to post the first
homework yet. I will do this over the long weekend, though. This way,
you may really enjoy the nonmathematical pleasures of it.
01/08/04: My office hours, just in case, will be 1:35-2:40 M
Th and by appointment. I will be happy to see you at any time, though.
01/07/04: The time and location of the course have
changed. The course will be meeting on Mondays and Thursdays from 3 to
4:30 p.m. in 509 Lake Hall.