Schedule

The course will be held online on Zoom.

• Lecture 1: Friday September 25, 2020, 10:00am - 12:00pm
  Crash course in algebraic topology: singular homology and co-homology, De Rham cohomology.
• Lecture 2: Monday September 28, 2020, 10:00am - 12:00pm
  The Morse homology theorem.
• Lecture 3: Tuesday September 29, 2020, 10:00am - 12:00pm
  Variational principle for Hamiltonian periodic orbits, action spectrum, the Conley-Zehnder index.
• Lecture 4: Wednesday September 30, 2020, 10:00am - 12:00pm
  Construction of the Floer homology groups for aspherical manifolds I.
• Lecture 5: Thursday October 1st, 2020, 4:30pm - 6:30pm
  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: Friday October 2, 2020, 10:00am - 12:00am
  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.

References

• Handwritten lecture notes
• M. Audin, M. Damian, Morse theory and Floer homology, Universitext. Springer, London; EDP Sciences, Les Ulis, 2014.
• A. Banyaga, D. Hurtubise, Lectures on Morse Homology,Kluwer Texts in the Mathematical Sciences, 29. Kluwer Academic Publishers Group, Dordrecht, 2004.
• D. Salamon, Lectures on Floer homology, Symplectic geometry and topology (Park City, UT, 1997), 143-229, IAS/Park City Math. Ser., 7, Amer. Math. Soc.
• D. Salamon, E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math., 45 (1992), 1303-1360.
• M. Schwarz, Morse homology, Progress in Mathematics, 111. Birkhauser Verlag, Basel.