Geometry of hyperconvex surface subgroups

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• Maria Beatrice Pozzetti (Università di Bologna)
• Thursday 04 September 2025, 10:15-11:15
• Seminar Room 1, Newton Institute.

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OGGW02 - Actions on graphs and metric spaces

A quasi-Fuchsian representation of a surface group in PSL is a discrete and faithful representation that preserves a Jordan curve on the Riemann sphere. These classical objects have a very rich structure as they lie at the crossroad of several areas of mathematics such as complex dynamics, Teichmüller theory, and 3-dimensional hyperbolic geometry. I will discuss joint work with James Farre and Gabriele Viaggi in which we investigate similar phenomena for a class of representations of surface groups in PSL , hyperconvex representations, and discuss geometric properties of the image subgroups and their parameter space. Among other things we show that the groups admitting hyperconvex  representations are virtually isomorphic to convex-cocompact subgroups of PSL , and more generally they exhibit striking analogies with such groups, such as suitable Ahlfors-Bers parameters.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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