Canonical diffusions on the pattern spaces of aperiodic Delone sets

Fractal Geometry and Dynamics

12 October 15:00 - 15:50

Michael Hinz - Bielefeld University

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.
Kenneth Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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