Limit Set Deformations Inside the Sphere at Infinity of the Complex Hyperbolic Plane

Surface group representations inside PU(2,1) share some geometric properties with Kleinian groups but also with real projective representations, related to divisible convex sets.
A central object for understanding their properties is the limit sets in the sphere at infinity. I will present computer generated figures of these limit sets that help build some intuition for deformations of real Fuchsian representations. This leads to a new tool for working with these deformations, which we call thinness.
Joint work (in progress) with E. Falbel and P. Will.

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