**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.

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