Morse Theory Reading Group

Fall 2003 Semester

Week 1: (Friday, October 10, 2003)

Introductory Meeting
PDF format file. Basic information for the reading group and notes from the meeting.

Week 2: (Friday, October 17, 2003)

Section 2: Definitions and Lemmas
PDF format file. Notes from the meeting.

The Rest of the Semester

I have not been very good about updating this web page. However, I hope to be better in the future. During the rest of the fall 2003 semester, we read up through section 10 of Milnor's Morse Theory.

Spring 2004 Semester

We begin the semester in Part III of Milnor's Morse Theory. We will streamline the presentations so that we can complete this book as quickly as possible. After we have finished, there is still some discussion as to what we will do. Options include inviting the faculty to lecture, reading more advanced Morse Theory (such as Milnor's Lectures on the h-Cobordism Theorem), or starting another book.

The reading group will meet on Fridays at 2:30 in the tea room of the Mathematics Building at Columbia University. Please send an e-mail to Shaffiq Welji if you would like to join the reading group.

Week 1

Friday, January 23, 2004
Review of Part III, Sections 11-13.

Week 2

Friday, January 30, 2004
Section 14: Jacobi Fields
Discussion led by Mr. D. McFeron.

Week 3

Friday, February 6, 2004
Section 15: The Index Theorem
Discussion led by Mr. J. Baldwin.

Week 4

Friday, February 13, 2004
Section 16: A Finite Dimensional Approximation to Ω^c
Discussion led by Mr. S. Welji.

Week 5

Friday, February 20, 2004
Section 17: The Topology of the Full Path Space
Discussion led by Mr. D. McFeron followed by
Section 18: Existence of Non-Conjugate Points
Very brief discussion led by Mr. J. Baldwin.

Week 6

Friday, February 27, 2004
Section 19: Some Relations between Topology and Curvature
Discussion led by Mr. J. Baldwin followed by
Section 20: Symmetric Spaces
Discussion led by Mr. S. Welji.

Week 7

Friday, March 5, 2004
Section 21: Lie Groups as Symmetric Spaces
Discussion led by Mr. D. McFeron.

Week 8

Friday, March 12, 2004
No meeting this week.

Spring Break: March 15, 2004 through March 19, 2004

Spring break is a chance for everyone to meditate on the Bott Periodicity Theorems (Sections 23 and 24).

Week 9

Friday, March 26, 2004
Section 22: Manifolds of Minimal Geodesics
Discussion led by Mr. J. Baldwin.

Week 10

Friday, April 3, 2004
Section 23: The Bott Periodicity Theorem for the Unitary Group and
Sections 24: The Periodicity Theorems for the Orthogonal Group
Group discussion.

Week 11

Thursday, April 9, 2004
Mr. M. Hedden lectured on Floer homology theory in a talk titled something along the lines of "A Leisurely Walk Through Floer Homology Theory."
Friday, April 10, 2004
J. Milnor, "On manifolds homeomorphic to the 7-sphere," Ann. Math. 64 (1956), 399--405.
Note that the above link only works on computers which have access to JSTOR. Discussion led by Mr. S. Welji.

Week 12

Tuesday, April 13, 2004
Mr. M. Hedden continued his lecture from April 9 with a talk about Ozsváth-Szabó Floer homology theory.
Thursday, April 16, 2004
Mr. T. Mrowka delivers this semester's J. F. Ritt lectures with a talk titled "Floer's Instaton Homology and Representations of Three Manifold Fundamental Groups."
Friday, April 17, 2004
R. Bott, "Morse thoery indomitable," Inst. Hautes Études Sci. Publ. Math. 68 (1988), 99--114.
Discussion led by Mr. D. McFeron.

Week 13

Friday, April 24, 2004
Mr. J. Morgan lectured about the h-Cobordism Theorem followed by a discussion led by Mr. J. Baldwin on
J. Morgan, "A Survey of Floer Homology Theories," to appear.

Week 14

Friday, May 1, 2004
Mr. M. Thaddeus lectured on some topic related to Morse theory.

Summer 2004

We plan to read J. Milnor's Lectures on the h-Cobordism Theorem this summer.