MT 832: Lagrangian submanifolds

Class on Monday, 3/24 will take place virtually at https://bccte.zoom.us/j/5219852726.

"Entrance exam." This is just a self-test for designed students who attended last semester's course.  It is a warm-up for this course, and I recommend actually sitting down and writing up your solutions.

Lecture 1, Jan 13. Gromov nonsqueezing (linear case).

Lecture 2, Jan 15. Gromov nonsqueezing (general case, part 1).

Lecture 3, Jan 22. Gromov nonsqueezing (general case, part 2.)

Lecture 4, Jan 24. Monotonicity theorem for holomorphic curves.

Lecture 5, Jan 27. The Chekanov torus (part 1).

Lecture 6, Jan 29.  The Chekanov torus (part 2).

Lecture 7, Jan 31.  The Chekanov torus (part 3).

Lecture 8, Feb 3.  The Chekanov torus (part 4).

Lecture 9, Feb 5.  The Chekanov torus (part 5).

Lecture 10, Feb 7.  Lagrangian surgery (after Polterovich) (part 1).

Lecture 11, Feb 10. Lagrangian surgery (part 2).

Lecture 12, Feb 12. Lagrangian surgery (part 3).

Lecture 13, Feb 14. Lagrangian surgery (part 4).

Lecture 14, Feb 17.  Lagrangian surgery (part 5).

Lecture 15, Feb 19.  Luttinger surgery (after Luttinger) (part 1).

Lecture 16, Feb 21.  Luttinger surgery (part 2).

Lecture 17, Feb 24.  Luttinger surgery (part 3).

Lecture 18, Feb 26.  Luttinger surgery (part 4).

Lecture 19, Feb 28.  Luttinger surgery (part 5).

Lecture 20, Mar 10. Luttinger surgery (part 6).

Lecture 21, Mar 12. Luttinger surgery (part 7).

Lecture 22, Mar 14. Luttinger surgery (part 8).

Lecture 23, Mar 17. Gromov's theorem on Lagrangians in C^n (part 1).

Lecture 24, Mar 19. Gromov's theorem (part 2).

Lecture 25, Mar 21. Gromov's theorem (part 3).

Lecture 26, Mar 24. Gromov's theorem (part 4).

Up next (with a dose of ambition): Floer homology, Oh's spectral sequence, Audin's conjecture for monotone tori, restrictions on monotone Lagrangians in C^3, Seidel's Lagrangian nonisotopic 2-spheres, and inscription problems.

Lecture 27, Mar 31.  Floer homology and Morse homology.

Lecture 28, Apr 2. Morse homology (part 2).

Lecture 29, Apr 4. Morse homology (differential).

Lecture 30, Apr 7.  Morse homology (towards invariance).

Lecture 31, Apr 9.

Lecture 32 recording, Apr 11.

Lecture 33, Apr 14.

Lecture 34, Apr 16.

Lecture 35, Apr 22. Floer homology (gradient flow).

Lecture 36, Apr 23.

Lecture 37, Apr 25.

Lecture 38, Apr 28.

Lecture 39, May 1.