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Topology/Geometry Seminar

Projective rigidity of circle packings

Francesco Bonsante (Università degli Studi di Pavia)

Location:  Online (See Zoom link)
Date & time: Tuesday, 24 October 2023 at 4:00PM - 5:00PM

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.

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