Oct 24

Title: Projective rigidity of circle packings

Speaker: Francesco Bonsante (Università degli Studi di Pavia)

Abstract: Observing that the notion of disk in CP^1 is invariant under projective transformations, Kojima, Mizushima and Tan proposed the study of circle packings on surfaces equipped with  complex projective structure. 

The main observation is that the combinatorially  a circle packing is described by a triangulation of the surface, called the nerve of the circle packing.

In the talk we will prove that for a fixed surface S of genus g bigger than one, and for a fixed triangulation T on S,  the moduli space of pairs (P,C), where P is a complex projective structure S and C is a circle packing with nerve equal to T, is naturally a manifold of dimension 6g-6.

We moreover prove that the circle packing is locally rigid, in the sense that there is no local deformation of C within a fixed projective surface P.

Results presented in the talk are part of a  collaboration with Michael Wolf.