Seminar

Speaker: Maxwell Plummer

Title: Free-by-cyclic groups via expanding semiflows

Abstract: For a 3-manifold M, a pseudo-Anosov suspension flow determines a face of its Thurston norm ball, and describes many ways M fibers over the circle. In this talk, we study a similar picture for a free-by-cyclic group G: we will construct a 2-complex with an expanding semiflow whose cross sections will determine the ways that G can split as a semidirect product. Time permitting, we will discuss the growth rates of the first return maps of these semiflows and relationships to endperiodic maps of infinite graphs.

Speaker: Junmo Ryang

Title: Convex cocompact and purely pseudo-Anosov subgroups of mapping class groups



Abstract: In 2002, Farb and Mosher introduced the notion of convex cocompactness in the mapping class group to capture coarse geometric information of the associated surface group extensions. Convex cocompact subgroups are necessarily finitely generated and purely pseudo-Anosov, but it is an open question whether the converse is true. On the other hand, there are certain subgroups of mapping class groups for which the converse is known to be true, including some classes of surface group extensions. In this short talk, we present some known results and some open questions in this setting.