09:00 to 10:00 Ian Leary (University of Southampton)Generalized Bestvina-Brady groups and their applications Co-authors: Robert Kropholler (Tufts University), Ignat Soroko (University of Oklahoma) In the 1990's Bestvina and Brady used Morse theory to exhibit (as subgroups of right-angled Artin groups) the first examples of groups that are but not finitely presented. The speaker has generalized this construction, via branched coverings, to construct continuously many groups of type , including groups of type FP that do not embed in any finitely presented group. I shall discuss the construction and some applications, including the theorem that every countable group embeds in a group of type and the construction of continuously many quasi-isometry classes of acyclic 4-manifolds admitting free, cocompact, properly discontinuous discrete group action (the latter joint with Robert Kropholler and Ignat Soroko). Related Linkshttps://arxiv.org/abs/1512.06609 - Archive link to preprint with main resulthttps://arxiv.org/abs/1610.05813 - Archive link to preprint on subgroups of groups INI 1 10:00 to 11:00 Yael Algom Kfir (University of Haifa)The boundary of hyperbolic free-by-cyclic groups Given an automorphism $\phi$ of the free group $F_n$ consider the HNN extension $G = F_n \rtimes_\phi \Z$. We compare two cases:1. $\phi$ is induced by a pseudo-Anosov map on a  surface with boundary and of non-positive Euler characteristic. In this case $G$ is a CAT(0) group with isolated flats and its (unique by Hruska) CAT(0)-boundary is a Sierpinski Carpet (Ruane).2. $\phi$ is atoroidal and fully irreducible. Then by a theorem of Brinkmann $G$ is hyperbolic. If $\phi$ is irreducible then Its boundary is homeomorphic to the Menger curve (M. Kapovich and Kleiner). We prove that if $\phi$ is atoroidal then its boundary contains a non-planar set. Our proof highlights the differences between the two cases above. This is joint work with A. Hilion and E. Stark. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Henry Wilton (University of Cambridge)Surface subgroups of graphs of free groups A well known question, usually attributed to Gromov, asks whether every hyperbolic group is either virtually free or contains a surface subgroup. I’ll discuss the answer to this problem for the class of groups in the title when the edge groups are cyclic.  The main theorem is a result about free groups F which is of interest in its own right: whether of not an element w of F is primitive can be detected in the abelianizations of finite-index subgroup of F.  I’ll also mention an application to the profinite rigidity of the free group. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 17:00 Free Afternoon 19:30 to 22:00 Formal Dinner at Christ's College