Student seminar on Floer theory and pseudoholomorphic curves
UC Berkeley, Fall 2003
We're taking a break at the moment (spring 2004) due to the large
number of advanced topology courses and lectures currently going on.
Organizer
Michael
Hutchings
hutching@math.berkeley.edu
Office phone: 510-642-4329.
Office: 923 Evans.
Office hours: TBA.
Goals
Floer theory and pseudoholomorphic curves and their applications to
low-dimensional and symplectic topology are currently the subject of
much active and exciting research. Participants in this seminar will
read recent research papers or essential background materials in the
area and give talks about them. Abundant questioning and discussion
is encouraged. The goal of the seminar is to get up to speed and keep
up with current research, learn more about the background that we are
supposed to know, and maybe think about new research topics. This
seminar was begun in Spring 2003 and will continue as long as there is
sufficient interest.
Prerequisites
In addition to basic knowledge of graduate-level geometry and
topology, the most important prerequisite is a strong motivation to
teach yourself stuff and ask questions. The lecture notes and
bibliography from the topics course that I taught in Fall 2002 (click here) could be helpful. If you
didn't follow all of that course or weren't around for it, don't
worry: now is your chance to really learn something! Like a soap
opera, one can jump into this seminar at any time; previous semesters
are not a prerequisite.
Spacetime coordinates
Wednesdays, 11:00-12:30, 959 Evans. Since the schedule is already
pretty full and we have a lot to do, we may sometimes have additional
talks at other times.
Suggested topics
Here is the handout from last semester
suggesting some possible starting points. Some of these were
discussed last semester but could be discussed further. You are free
to do other things, and I am happy to meet with you individually to
help you select a specific topic.
I mentioned some additional references in the first meeting on 9/3.
Namely, Seidel's lecture notes that he recently posted on the preprint
server, Seidel's paper about knotted Lagrangians, Bourgeois's lecture
notes about contact homology / SFT and his preprint about families of
contact structures, the Fukaya-Oh paper in Asian J. Math, Fukaya's
paper about the Casson invariant and the theta graph, and the
Siebert-Tian paper about unknottedness of symplectic surfaces in CP^2.
Schedule of talks
- 2003/9/3. Organizational meeting.
- 9/10. Hutchings: Finite type invariants of knots and 3-manifolds.
- 9/17. Eli Grigsby: Finite type invariants and counting graphs.
- 9/24. ???
- 10/1. Yao: Lagrangian spheres in S^2 x S^2 (Hind's preprint).
- 10/8. Wang: Fukaya-Oh's paper.
- 10/15. Wang, continued.
- 10/22. Cotton: Seiberg-Witten Floer and genus bounds.
- 10/29. Cotton: continued.
- 11/5. Y. Chen: Introduction to contact homology.
Talks from the previous semester
- 2003/1/23. Organizational meeting.
- 1/31. Tamas Kalman: relative contact homology.
- 2/7. Tom Mark: bubble-tree compactification.
- 2/14. Tamas Kalman: relative contact homology, part 2.
- 2/21. Eli Grigsby: Floer's exact triangle.
- 2/28. Eli Grigsby: Floer's exact triangle, part 2.
- 3/14. David Farris: Gluing Floer flow lines.
- 3/21. No meeting.
- 4/4. Michael Hutchings: Floer homology of families.
- 4/11. David Farris: Gluing Floer flow lines II.
- 4/18. Eli Grigsby and Tamas Kalman: Coherent orientations.
- 4/25. Xiang Tang: Fukaya category.
- 5/2. Jiangang Yao: Intersection positivity.