Time: Tuesday, Feb 20, 2018, 2:00pm @ MTH3207

Speaker: Patricia Alonso-Ruiz (UConn)

Title: Heat diffusion on inverse limit spaces

Abstract: Inverse (or projective) limits give rise to a wide range of spaces that can show remarkably different properties. The present talk aims to illustrate how different the (in some sense natural) diffusion processes occurring on them can be by looking at two examples: a parametric family of diamond fractals and pattern spaces of aperiodic Delone sets. On a generalized diamond fractal, a canonical diffusion process can be con- structed following a procedure proposed by Barlow and Evans for inverse lim- its of metric measure spaces. The associated heat semigroup has a kernel, of which many properties have been studied by Hambly and Kumagai in the case of constant parameters. It turns out that in general it is possible to give a rather explicit expression of the heat kernel, that is in particular uniformly continuous and admits an analytic continuation. In contrast, pattern spaces feature quite an opposite scenario. Regarded as compact metric measure spaces of a suitable type, one can introduce a diffusion process with an especially simple expression whose associated heat semigroup has no density, that is a heat kernel, with respect to the natural measure of the space.
Back to seminar