Michael Hinz: Canonical diffusions on the pattern spaces of aperiodic Delone sets

In this talk we consider differential operators and diffusion processes on pattern spaces of aperiodic Delone sets. Such spaces arise naturally in tiling theory and diffraction theory, and they have features of both manifolds and fractals. We first discuss Feller properties. Assuming unique ergodicity we then study items of a related $L^2$-theory, such as properties of self-adjoint Laplacians and Dirichlet forms, the non-existence of heat kernels or Liouville theorems. The results are joint with P. Alonso-Ruiz, A. Teplyaev and R. Trevino.