Inaugural Talk: Wednesday 6 May 2020, 12:00 AEST Henry Segerman (Oklahoma State University) Title: From veering triangulations to link spaces and back again Abstract: Agol introduced veering triangulations of mapping tori, whose combinatorics are canonically associated to the pseudo-Anosov monodromy. In unpublished work, Guéritaud and Agol generalise an alternative construction to any closed manifold equipped with a pseudo-Anosov flow without perfect fits. Schleimer and I build the reverse map. As a first step, we construct the link space for a given veering triangulation. This is a copy of R^2, equipped with transverse stable and unstable foliations, from which the Agol-Guéritaud construction recovers the veering triangulation. The link space is analogous to Fenley’s orbit space for a pseudo-Anosov flow. Along the way, we construct a canonical circular ordering of the cusps of the universal cover of a veering triangulation. I will also talk about work with Giannopolous and Schleimer building a census of transverse veering triangulations. The current census lists all transverse veering triangulations with up to 16 tetrahedra, of which there are 87,047. ============================================ For access detail, to join the mailing list, and a weekly schedule, see https://sites.google.com/view/agtw/home