**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)

Register at the following link:https://prev-www.math.unipd.it/userlist/subscribe/?idlist=457