• Seminar Meetings: MTh 12-1 in 762 Evans or MSRI
• Course Control Number: 15773

• [A] Symplectic Cohomology & Viterbo's Theorem by M. Abouzaid. Arxiv Preprint.
• [AD] Morse Theory & Floer Homology by M. Audin & M. Damien. Springer-Universitext.
• [B] Lectures On Symplectic & Contact Homology by F. Bourgeois. Gokova Lecture Notes.
• [DS] Self-Dual Instantons & Holomorphic Curves by S. Dostoglou & D. Salamon. Annals Of Math.
• [MS] J-holomorphic Curves & Symplectic Topology by D. McDuff & D. Salamon. AMS Publications.
• [O1,O2] Symplectic Topology & Floer Homology Volumes 1 & 2 by Y-G. Oh. Cambridge Press.
• [PSS] Symplectic Floer-Donaldson theory And Quantum Cohomology by S. Piunikgin, D. Salamon & M. Schwarz
• [RS] The Spectral Flow & The Maslov Index by J. Robbin & D. Salamon.
• [Se] Fukaya Categories & Picard-Lefschetz Theory by P. Seidel. EMS Publications.

This seminar will be a reading seminar, working through the book Morse Theory & Floer Homology . We will meet twice a week to discuss that weeks reading. Time permitting, we will study some additional topics in Floer theory: additional structure on the Floer groups, the PSS isomorphism, Lagrangian Floer theory, advanced regularization techniques, and other Floer homology theories in low-dimensional topology and contact geometry are among the candidates.

• M 1.22: Arnold conjecture, Hamiltonian Floer theory [AD] § 6
• Th 1.25: Maslov/CZ index I. [AD] § 7.1-7.2
• M 1.29: Maslov/CZ index II. [AD] § 7.3
• Th 2.1: spectral flow I. [RS] p 1-25
• M 2.5: spectral flow II. [RS] p 25-40
• Th 2.8: spaces of j-curves and perturbations. [AD] § 8.1-8.3
• M 2.12: linearization, Fredholm index, decay. [AD] § 8.4,8.7-8.9
• Th 2.16: transversality, somewhere injectivity. [AD] § 8.5,8.6
• M 2.19: no meeting - academic holiday
• Th 2.22: spaces of trajectories. [AD] § 9.1-9.3
• M 2.26: gluing map: immersion property. [AD] § 9.4-9.5
• Th 3.1: gluing map: uniqueness property. [AD] § 9.6
• M 3.5: moduli space orientations. [Sa] § A.1, [Se]
• Th 3.8: coherent orientations, gluing with orientations [Se] § 11
• M 3.12: Floer/Morse isomorphism. [AD] § 10
• Th 3.15: invariance I: defining the morphism. [AD] § 11.1-11.2
• M 3.19: invariance II: [AD] § 11.3-11.4
• Th 3.22: invariance III: conclusion [AD] § 11.5-11.6
• M 3.26, Th 3.29: no meetings - spring break
• M 4.2: analytical loose ends [AD] § 12,13
• Th 4.5: Arnold chord conjecture, Lagrangian Floer theory. [O]
• M 4.12: LFH general definition. [O2] § 13
• M 4.16: j-curves with bdry: cusps, chain maps. [O2] § 14.1-14.2
• Th 4.19: j-curves with bdry: cusps, chain maps. [O2] § 14.3-14.4
• M 4.23: space of trajectories, Fredholm index. [O2] § 15.1-15.3
• Th 4.26: (coherent) orientations, gluing. [O2] § 15.4-15.6
• Th 4.30: operations in Floer theory I
• M 5.3: operations in Floer theory II