Finding a totally geodesic surface, an embedded surface where the geodesics in the surface are also geodesics in the surrounding manifold, has been a problem of interest in the study of 3-manifolds. This has especially been of interest in hyperbolic 3-manifolds and knot complements, complements of piecewise-linearly embedded circles in the 3-sphere. This is due to Menasco-Reid's conjecture stating that hyperbolic knot complements do not contain such surfaces. Here, we present an algorithm that determines whether a given surface is totally geodesic and an algorithm that checks whether a given 3-manifold contains a totally geodesic surface. We applied our algorithm on over 150,000 3-manifolds and discovered nine 3-manifolds with totally geodesic surfaces. Additionally, we verified Menasco-Reid's conjecture for knots up to 12 crossings.

As large collections of historically significant recorded speech become increasingly available, scholars are faced with the challenge of making sense of what they hear. This paper proposes automatically linking conversational speech to related resources as one way of supporting that sense-making task. Experiment results with transcribed conversations suggest that this kind of linking has promise for helping to contextualize recordings of detail-oriented conversations, and that simple sliding-window bag-of-words techniques can identify some useful links.