In-Person and Online Talk

In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, completing the work first initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. A well-known proof of this theorem is due to Bers, who rephrased the problem in terms of extremal quasiconformal maps between complex surfaces. In joint work with Camille Horbez, we revisit Bers's approach but from the point of view of hyperbolic geometry. This gives a new proof of the classification theorem, as well as new representatives for pseudo-Anosov homeomorphisms as extremal Lipschitz maps between hyperbolic surfaces.