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.
Atkinson will speak about:
Title: Small volume link orbifolds
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.
Malestein will speak about:
Title: On genericity of pseudo-Anosovs in the Torelli group
Abstract: We will show that, for any (symmetric) finite generating set of the Torelli group of a closed surface, the probability that a random word is not pseudo-Anosov decays exponentially in the length of the word; i.e. a random walk in the Torelli group is exponentially unlikely not to be pseudo-Anosov. As a consequence of our methods, we will prove the same statement for some other finitely generated subgroups of the mapping class group. Joint work with Juan Souto.
Nakamura 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 with genus and with some conical singularities of positive curvatures, its Fuchsian polyhedral realization is an incompressible isometric embedding of in a Fuchsian cylinder for some Fuchsian group with genus such that the image is a piecewise totally geodesic polyhedral surface. It is known by a theorem of Fillastre that, for any such , there exists a unique convex Fuchsian polyhedral realization. We will describe the geometry of convex and non-convex Fuchsian polyhedral realizations when has a single conical singularity, and show that the convex case indeed corresponds to the Delaunay triangulation of . Joint work with Jaejeong Lee.