Date: 4 November 2016, 4:30pm Location: Hempfield High School, Room 213 Speaker: Carl Droms, James Madison University Title: Planar Cayley Graphs Abstract. Which groups have Cayley graphs that are planar? This question was answered for finite groups in 1896. Infinite groups having Cayley graphs that can be embedded in the plane without vertex accumulation points (VAPs) are also well-understood. We will discuss one approach to classifying the groups whose Cayley graphs can be embedded in the plane, but only with one or more VAPs. As an application, we obtain a complete classification of the ones that can be embedded with a single VAP.