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Title:
Diffusions on singular spaces
Speaker:
Abstract:
On many classical fractal spaces, such as the Sierpinski triangle and square, there are natural and essentially unique diffusion processes which do not obey the classical Einstein relation: the distance traveled by the diffusion is not proportional to the square root of time. However, there are uniquely defined spectral and walk dimensions which determine the behavior of these diffusion processes via so called generalized Einstein relation. Surprisingly, these dimensions appeared recently in the physics theories of the quantum gravity involving theoretical and numerical analysis of the casual dynamical triangulations. If time permits, I'll also briefly describe singular diffusions on the pattern spaces of aperiodic Delone sets, e.g. a quasicrystal lattice or a Penrose tiling (a joint work with Patricia Alonso-Ruiz, Michael Hinz and Rodrigo Trevino). The presentation will be non-technical, and no prior knowledge about fractals or diffusion processes will be assumed.
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