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       April 11, 2007:     Veronique Godin
                                 "From Morse Theory to Floer Homology" 

       April 18, 2007:      Matt Gelvin
                                   "Introduction to Heegaard Floer Homology"

      April 25, 2007:      Matt Hedden
                                   "First Computations of Heegaard Floer Homology"

      May 2, 2007:         Brett Parker
                                   "Gromov Compactness"

      May 9, 2007:         Veronique Godin
                                   "A-Infinity Categories and Morse Theory of Finite Dimensional Manifolds"

      May 16, 2007:       Mohammed Abouzaid
                                   "The Fukaya Category of the Cotangent Bundle of a Smooth Manifold"

References:

• A survery article by Dusa McDuff.
• Various notes on Heegaard Floer homology.
• Two articles (here and here) by Abbondandolo and Schwarz on the correspondence between the homology of the free loop space on M and
  the Floer homology of the cotangent bundle of M.
• An article by Peter Kronheimer and Ciprian Manolescu.
  
• Two articles (here and here) on Fukaya categories by Paul Seidel.