## Seminar November 22 – Kei Nakamura

On November 22nd, Kei Nakamura will speak in the the Geometry-Topology Seminar. He will speak about:

Title: On convex and non-convex Fuchsian polyhedral realizations of hyperbolic surfaces with a single conical singularity

Abstract: For a hyperbolic surface $S$ with genus $g \geq 2$ and with some conical singularities of positive curvatures, its Fuchsian polyhedral realization is an incompressible isometric embedding of $S$ in a Fuchsian cylinder $H^3/\Gamma$ for some Fuchsian group $\Gamma$ with genus $g$ such that the image is a piecewise totally geodesic polyhedral surface. It is known by a theorem of Fillastre that, for any such $S$, there exists a unique convex Fuchsian polyhedral realization. We will describe the geometry of convex and non-convex Fuchsian polyhedral realizations when $S$ has a single conical singularity, and show that the convex case indeed corresponds to the Delaunay triangulation of $S$. Joint work with Jaejeong Lee.

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