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 (less than 10 pages) and a 10 minute recorded presentation (in any format the student finds convenient and appropriate).
Students will work in groups to review and give comments on a draft version of the project.
Timeline:
By March 8th, students will have
By March 15th, students will have
Students are free to choose their own group, but I will help with setting up groups if you email me.
The final version of the project is due April 23rd.
Ideas for projects
Generating functions and recurrence (CdS Ch. 4-5)
Contact geometry (CdS Ch. 10-11)
There are probably multiple projects in here, for example, focusing more on dynamics (Lectures on controlled Reeb dynamics, Geiges) or on low-dimensional topology (Introductory Lectures on Contact Geometry, Etnyre)
The non-squeezing theorem and pseudoholomorphic curves (a good place to start is Wehrheim's course, video and notes)
Related to that is the theory of symplectic capacities (these notes of Rezakhanlou are for a course on symplectic geometry that emphasizes capacities)
Hodge theory and the proof of hard Lefschetz (Complex Algebraic Geometry, Gallier and Shatz, Sections 2.5-6)
Student(s): Brady Ali Medina, Alexandre Zotine, Charalambos Kioulos
Convexity for moment map images (CdS, Ch. 27; Chapter 7 of Dwivedi, et. al.)
The Duistermaat-Heckman theorem (CdS, Ch. 30; Chapter 10 of Dwivedi, et. al.)
Student(s): Hank Chen
Applications to specific physics problems (for example, this course on celestial mechanics may contain some interesting examples, as may this paper of Lin and Marsden)
Student(s): Robert Harris
The Calabi conjecture (one intro here: https://arxiv.org/pdf/1703.06945.pdf; Joyce’s book “Compact Manifolds with Special Holonomy” might also be a good source, but I don’t have an electronic copy)
Student(s): Aiden Patterson