PhD Course in Padua (via zoom): Introduction to Floer Homology

September 13, 2020 [expired]

Title of the course: “Introduction to Floer Homology”

Lecturer: Marco Mazzucchelli (CNRS & ENS Lyon)

Syllabus:

Lecture 1: Crash course in algebraic topology: singular homology and cohomology, DeRham cohomology.

Lecture 2: The Morse homology theorem.

Lecture 3: Variational principle for Hamiltonian periodic orbits, action spectrum, the Conley-Zehnder index.

Lecture 4: Construction of the Floer homology groups for aspherical manifolds I.

Lecture 5: Construction of the Floer homology groups for aspherical manifolds II, proof of the Arnold conjecture on the fixed points of generic Hamiltonian diffeomorphisms.

Lecture 6: Bott’s iteration formula for the Conley-Zehnder index, proof of the Conley conjecture on the periodic points of generic Hamiltonian diffeomorphisms of aspherical manifolds. Bonus arguments: Floer homology for monotone manifolds, products in Floer homology, spectral invariants, symplectic homology, etc.

Timetable of the lectures (12 hrs):

Friday Sept 25, 2020, 10:00 - 12:00

Monday Sept 28, 2020, 10:00 - 12:00

Tuesday Sept 29, 2020, 10:00 - 12:00

Wednesday Sept 30, 2020, 10:00 - 12:00

Thursday Oct 1st, 2020, 16:30 - 18:30

Friday Oct 2, 2020, 10:00 - 12:00

Note: The course will be held online via Zoom (the link to the meeting will be send to the participant some day before the start of the course)