Symplectic Geometry

This class will be offered as part of the first edition of the OSU Graduate Math Summer Mini-courses, 2021.

"Syllabus". The mini-course will be roughly divided in three parts:

• Symplectic Linear Algebra (~1 week);
  • Lecture 1.
  • Lecture 2.
• Symplectic Manifolds (~2 weeks);
  • Lecture 3.
  • Lecture 4.
  • Lecture 5.
  • Lecture 6.
• Hamiltonian Actions (~1 week 2 weeks).
  • Lecture 7.
  • Lecture 8.
  • Lecture 9.
  • Lecture 10.

I do not know if we'll be able to cover all the material I'd like to in four weeks. We might need an extra week. Let's cross that bridge when we come to it. We managed with five weeks.

Schedule: We will have two lectures per week, on Tuesdays from 5 p.m. to 6 p.m. and on Wednesdays from 3 p.m. to 4 p.m., starting on June 15th, in room MW154.

Some references: There are many references listed on the notes. The ones below besides the main lecture notes are the ones I particularly like and could find legally available either on arXiv or on the author's webpages.

• Lecture notes written by me specifically for this course.
• Cannas da Silva, A.; Symplectic Geometry - overview written for the Handbook of Differential Geometry, vol. 2, 2004.
• Meinrenken, E.; Symplectic Geometry, Lecture Notes, University of Toronto, 2000.
• Holm, D. D.; Geometric Mechanics - Part I: Dynamics and Symmetry, 2nd edition, Imperial College Press, 2011.

Observation: If you find any mistakes on the main lecture notes, please let me know. If you're watching the videos at any moment and see that I made a mistake on the spot, also let me know. For instance, around minute 13 of Lecture 2, in the remark made in blue, obviously "compact symplectic manifolds" should read only "compact manifolds", etc. Hopefully I won't screw up often enough to justify making an actual errata for the videos.