Math 7620 - Seminar in Geometry - Symplectic Geometry (Spring 2014)

Instructor: Ana Rita Pires

Email: apires [at] math . cornell .edu

Office: Malott 581

Schedule: Tuesdays and Thursdays 2:55-4:10pm at Mallot 230 (we will end early on Thursdays to accommodate those attending the Oliver Club)

Office Hours: Wednesday 1:30-2:30pm or by appointment

Syllabus           (Evolving) list of possible topics for student presentations


[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

quantum cohomology and mirror symmetry

and on Thursday Luís Diogo will do the same for

flexibility and rigidity in symplectic and contact geometry.

[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.

DateWhat we coveredSuggested problems Reading for next lecture
Jan 23Chapter 1HW1 Problems 1-7Chapter 2
Jan 28Chapter 2 and 3.1HW2 Problems 1,2Chapter 3
Jan 30Chapter 3HW4 (read Chapter 4 first)no class on Tuesday
Feb 4no classChapter 6
Feb 6Chapter 6Chapter 7
Feb 11Chapter 7 and 8.1HW6 Problem 3Chapters 8 and 9
Feb 13Chapter 8 and most of 9no class on Tuesday
Feb 18February break, no classChapters 10 and 11
Feb 20Chapters 9 and 10HW 7Chapters 11 and 12
Feb 25Chapters 11 and (most of) 12HW8Chapters 13 and 14
Feb 27End of chapter 12 and chapters 13 and 14HW9 and HW10Chapters 15 and 16
Mar 4Chapters 15 and 16.1-3HW11Chapter 17 and 18.1
Mar 6Chapters 16.4 and 17.1-3HW12Chapters 18.1, 18.3 and 21
Mar 11Chapters 18.1, 18.3 and 21HW16Chapter 22
Mar 13Chapter 22HW17
Mar 18Guest lecturer: Nick Sheridan
Mar 20Guest lecturer: Luís DiogoChapter 23
Mar 25Chapter 23Chapter 24
Mar 27Chapter 24HW19 and HW20
Apr 1 Spring break
Apr 3 Spring breakChapter 27
Apr 8Chapter 27HW21Chapter 28
Apr 10Chapter 28Chapter 29
Apr 15Chapter 29HW22Chapter 30
Apr 17
Apr 22My's presentation
Apr 24Zhexiu's presentation
Apr 29Drew's presentation
May 1Hung's presentation
May 6Ahmad'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.