Math 7620 - Seminar in Geometry - Symplectic Geometry (Spring 2014)
[May 1] Next Tuesday, at the usual class time, Ahmad Rafiqi will be talking about Poisson geometry.
[May 1] Here is the paper that Hung Tran's talk focused on.
[Apr 30] Tomorrow, Hung Tran will talk about circle actions on 4-dimensional manifolds. Schedule is 2:40pm-3:55pm.
[Apr 30] Sources from Drew Zemke's talk on 3-dimensional contact topology: these and these.
[Apr 24] Next time, Drew Zemke will be talking about 3-dimensional contact topology. It falling on a Tuesday, the schedule is as usual.
[Apr 24] Notes from Zhexiu Tu's lecture about Legendrian knots and differential algebras: PDF .
[Apr 22] Next time, Zhexiu Tu will be talking about Legendrian knots, etc.. The schedule will be 2:40pm-3:55pm.
[Apr 22] Notes from My Huynh's lecture about the nonsqueezing theorem, the symplectic camel theorem and symplectic capacities: PDF .
[Mar 20] Notes from Luis Diogo's lecture about flexibility and rigidity in symplectic and contact geometry: PDF.
[Mar 18] Notes from Nick Sheridan's lecture about mirror symmetry: PDF.
[Mar 17] This week we have two guest lecturers: on Tuesday, Nick Sheridan will give a gentle introduction to
and on Thursday Luís Diogo will do the same for
[Feb 18] I will be out of town tomorrow Wednesday Feb 19, so regular office hours are cancelled this week.
[Feb 6] Posted new and improved list of presentation topics (mostly added references). When you decide on a topic, from the list or otherwise, let me know.
[Feb 6] In response to the question "Why do we care about Lagrangian submanifolds?", see the box with all caps in page 5 of this article of Weinstein's.
[Jan 23] Added Syllabus and (evolving) list of possible topics for student presentations. If you have suggestions for topics, send them along!
[Jan 11] Webpage exists.
The homework is not to be handed in, but you should work on it. As for the reading, you should (at least) skim the sections assigned.
| Date | What we covered | Suggested problems | Reading for next lecture |
|---|---|---|---|
| Jan 23 | Chapter 1 | HW1 Problems 1-7 | Chapter 2 |
| Jan 28 | Chapter 2 and 3.1 | HW2 Problems 1,2 | Chapter 3 |
| Jan 30 | Chapter 3 | HW4 (read Chapter 4 first) | no class on Tuesday |
| Feb 4 | no class | Chapter 6 | |
| Feb 6 | Chapter 6 | Chapter 7 | |
| Feb 11 | Chapter 7 and 8.1 | HW6 Problem 3 | Chapters 8 and 9 |
| Feb 13 | Chapter 8 and most of 9 | no class on Tuesday | |
| Feb 18 | February break, no class | Chapters 10 and 11 | |
| Feb 20 | Chapters 9 and 10 | HW 7 | Chapters 11 and 12 |
| Feb 25 | Chapters 11 and (most of) 12 | HW8 | Chapters 13 and 14 |
| Feb 27 | End of chapter 12 and chapters 13 and 14 | HW9 and HW10 | Chapters 15 and 16 |
| Mar 4 | Chapters 15 and 16.1-3 | HW11 | Chapter 17 and 18.1 |
| Mar 6 | Chapters 16.4 and 17.1-3 | HW12 | Chapters 18.1, 18.3 and 21 |
| Mar 11 | Chapters 18.1, 18.3 and 21 | HW16 | Chapter 22 |
| Mar 13 | Chapter 22 | HW17 | |
| Mar 18 | Guest lecturer: Nick Sheridan | ||
| Mar 20 | Guest lecturer: Luís Diogo | Chapter 23 | |
| Mar 25 | Chapter 23 | Chapter 24 | |
| Mar 27 | Chapter 24 | HW19 and HW20 | |
| Apr 1 | Spring break | ||
| Apr 3 | Spring break | Chapter 27 | |
| Apr 8 | Chapter 27 | HW21 | Chapter 28 |
| Apr 10 | Chapter 28 | Chapter 29 | |
| Apr 15 | Chapter 29 | HW22 | Chapter 30 |
| Apr 17 | |||
| Apr 22 | My's presentation | ||
| Apr 24 | Zhexiu's presentation | ||
| Apr 29 | Drew's presentation | ||
| May 1 | Hung's presentation | ||
| May 6 | Ahmad's presentation |
We will start with basics by following Ana Cannas da Silva's Lectures on Symplectic Geometry, 2008 edition (available here through the math library). It being a seminar, some lectures will be given by the instructor, others by the students (here is an evolving list of possible topics, feel free to suggest more!). We might also have guest lecturers.