This is where I will be posting the homeworks.
HW#1 (due in class or by email by Tuesday, February 22):
1. Fill in the details of the argument given in class, that Sp(2n) \cap O(2n) = U(n). If you need to recall the general structure of the argument, have a look at the lecture notes, Lemma 5.8.
2. Do the exercise, regarding Cartan’s Magic Formula, on p. 44 of the Ana Canas da Silva lecture notes here. Only do it for “autonomous” vector fields, that is vector fields that do not depend on time.
3. Do HW#6, Problem #1, on p. 58 of the above Ana Canas da Silva notes.
4. Bonus: Problem #2, HW#6, in the same notes.
HW#2 (due by email by Tuesday, March 29):
1. McDuff-Salamon, Exercise 4.1.16
2. McDuff-Salamon, Exercise 4.3.5(i)
3. Chen, Exercise 1.4.
4. Bonus, give a proof of Proposition 1.5 in the link for problem 3. It’s better if you try it yourself, but if you just end up writing out the proof there, that’s fine. Just make sure to understand it!
HW#3 (due by email by Tuesday, May 3):