Title:  Heegaard Floer homology and fibred three-manifolds.

Abstract:  Heegaard Floer homology is a theory introduced by Ozsvath and
Szabo as an analogue to Seiberg-Witten theory. For knots in 3-manifolds,
this theory is refined to a filtered version, called knot Floer homology.
Ozsvath and Szabo conjectured that knot Floer homology detects fibred
knots in the three-sphere. In this talk, we will discuss a proof of this conjecture,
based on the works of Paolo Ghiggini and of the speaker. In fact, one can
show that Heegaard Floer homology detects whether a 3-manifold is fibred,
namely, whether it is a surface bundle over the circle. Some applications
will also be discussed.