Approaches to tiling semigroups (Nick Gilbert, NBSAN York, 25th November 2009)

Abstract: Tiling semigroups are inverse semigroups whose elements are constructed from finite pieces of a tiling of R^n. A lot is understood about their general structure, thanks to work of Kellendonk, Lawson, Zhu and others. There's a great deal still to be done in exploring relationships between the geometry of a particular class of tilings and the associated tiling semigroups. In this talk, we'll look at some recent approaches to this area, including work of Almeida and McAlister on presentations and connections with formal language theory, and some further structural results (joint work with Erzsi Dombi) that connect tiling semigroups with HNN extensions, and that even find something interesting to say about the periodic case in dimension one.