## Atkinson, Malestein, Nakamura speak at Joint Meetings

Our research group is well-represented at the Joint AMS-MAA National Meetings taking place this week in Boston. Dave Futer is co-organizing a special session, while Chris Atkinson, Justin Malestein, and Kei Nakamura are all giving talks.

Abstract: We will discuss recent investigations of small volume hyperbolic 3–orbifolds with singular locus a link. In the special case where the singular locus is a knot in the 3–sphere, we identify the smallest volume example. We will also describe more general results on lower volume bounds for hyperbolic 3–orbifolds with singular locus a link and identify the smallest volume example in certain cases. Joint work with Dave Futer.

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.