Speaker: Eric Bedford
Title: Automorphisms of the Plane
Affiliation: Indiana University
Date: Friday, February 15, 2008
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. We will describe some joint work with Kyounghee Kim about invertible mappings of the (projective) plane. The maps themselves are easy to write down, but the formulas have singularies. On the other hand, there is the "blowing-up" operation that is useful for removing singularities. We show that in certain cases, the blowing up can be performed in a way that produces dynamical systems without singularities. These are automorphisms of the plane (after blowups).
In particular, we are able to construct mappings with positive entropy. It had been conjectured at one point that there might only be finitely many rational surfaces with automorphisms of positive entropy, and subsequent works of McMullen and ourselves had shown that there was a countable family of examples. Here we give examples which vary continuously with a finite number of parameters.