Diff. Geom, Math. Phys., PDE Seminar: Antoine Julien

In this talk, I will give an introduction to aperiodic tilings. Usually, one studies a topological dynamical system associated to these tilings rather than one specific tiling (this is the analogue to studying a subshift rather that one single word in symbolic dynamics). It is a natural question to ask what happens to the underlying tilings when there is a homeomorphism between tiling spaces. The result I will present is the following: whenever two tiling spaces are homeomorphic, the complexity function is preserved up to some multiplicative constants and rescaling.