Heegaard surfaces and measured laminations

A Heegaard splitting is a decomposition of a 3-manifold into a pair of
handlebodies along an embedded surface, called Heegaard surface. Every
closed 3-manifold has a Heegaard splitting. The Waldhausen conjecture says
that a 3-manifold has only a finite number of inequivalent minimal (or
irreducible) Heegaard splittings. We will study the limit of a sequence of
compact surfaces in the measured lamination space, and give a complete
solution to the Waldhausen conjecture.

The colloquium will present the general background and ideas of this approach.