This is a working group that meets on Thursdays from 2:00 to 4:00, in EOSB 4127 (that is, at PIMS). In the first part we will go through the definition of Heegaard Floer homology, with a view to surveying some of the more recent literature in the second part. The aim is to be introductory, and participation will be encouraged but perhaps not required. Graduate students are particularly welcome.
There are various sources that serve as a point-of-entry to the subject. For instance, Ozsváth and Szabó's Introduction to Heegaard Floer homology and Lectures on Heegaard Floer homology provide a good starting point. For a better idea of where this machinery comes from, I think that McDuff's survey Floer theory and low dimensional topology does a great job.
Our focus is on a particular invariant of three-manifolds, and the applications of this machinery that have followed, and as such some definition and constructions from three-manifold topology will be needed. For background on three-manifolds, I recommend starting with Rolfsen's book Knots and Links – a UBC homegrown classic. For a very recent reference emphasizing the interactions with group theory and incorporating recent developments such as Perelman's Geometrization Theorem, see Aschenbrenner, Friedl, and Wilton's book 3-manifold groups.