Description: This class covers the basic theory of symplectic manifolds. Symplectic structures play a key role in modern mathematics and physics. We will discuss their basic local theory (in particular, the Darboux theorem), connections to complex and Kähler geometry, Hamiltonian mechanics, moment maps and symplectic reduction, and some additional topics, such as toric varieties, hyperkähler structures, quantization, Fukaya categories and mirror symmetry.
Prerequisites: Familiarity with the basics of differential geometry: smooth manifolds, tangent vectors and forms. In particular, exterior and Lie derivatives will play an important role. Some knowledge of Lie groups and Lie algebras will also help, though we will briefly discuss the required background.
There is a course outline which covers essentially the same information as below.
Fields Academy: The course will be available online through Fields Academy. It is free and should be available for credit for students at Fields "Principal Sponsoring Universities." It is also open to other students around the world; Fields does ask for a CAD$100 fee for the course. If paying this fee is an issue for you, email me, and I will see about covering it out of my grant (obviously, this is not a guarantee, since I only have so much grant).
Register at: https://zoom.us/meeting/register/tJcud-uqqD8jGdFAiuhtamPqtArOUQUjpGW_
Note: even if you are officially registered through UW, you should also do the Zoom registration.
Instructor: Ben Webster (email@example.com)
TA: Justin Hilburn (firstname.lastname@example.org)
Lecture times: Mondays & Wednesdays, 1pm-2:30pm; classes will be held over Zoom.
Text: Lectures on Symplectic Geometry ****by Ana Cannas da Silva.
Marking: There will be 5 assignments (roughly one every two weeks) and a final project. The assignments will be worth 50% of the grade and the project will also be worth 50%.
HW: HW will be posted on, and submitted through Crowdmark.
Final project: The final project will cover an additional topic related to the course. The topic will be the student's choice, subject to instructor approval. The project will consist of a short paper and a 10 minute recorded presentation (in any format the student finds convenient and appropriate). Students will be placed into pairs to review and give comments on a draft version of the project. For more info:
Course dates: Jan 11-Apr 12, 2021