Title: Rational open books and Heegaard Floer contact invariants

Abstract: Giroux's correspondence between contact structures and open books is of fundamental importance in 3-dimensional contact topology. Rational open books, introduced by Baker-Etnyre-Van Horn-Morris, are an extension of the classical notion. I will explain how to compute the Ozsvath-Szabo contact invariants of contact 3-manifolds given by rational open books, and discuss some applications. In particular, our results yield tight contact structures on manifolds obtained by large integral surgeries on certain knots. (Joint with M. Hedden.)