Fractals 6 Slides

On Saturday, I will be presenting some of my recent work, which extends Michel Lapidus’s theory of complex dimensions in $$\mathbb{R}^n$$ to a larger class of homogeneous metric measure spaces. In particular, I will be discussing the complex dimensions of subsets of $$p$$-adic sets. In case they should become necessary: slides for Fractals 6.

Abstract: The higher dimensional theory of complex dimensions developed by Lapidus, Radunović, and Žubrinić provides a language for quantifying the oscillatory behaviour of the geometry of subsets of $$\mathbb{R}^n$$. In this talk, we will describe how the theory can be extended to metric measure spaces that meet certain homogeneity conditions. We will provide examples from $$p$$-adic spaces and discuss the geometric information that can be recovered from the complex dimensions in these cases.

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