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Undecidable properties of self-affine sets and multitape automata

Timo Jolivet ( Institut de Mathématiques de Toulouse, Université Paul Sabatier )

We study the decidability of the topological properties of some objects coming from fractal geometry.  We prove that having empty interior is undecidable for the sets defined by two-dimensional graph-directed iterated function systems.  These results are obtained by studying a particular class of self-affine sets associated with multi-tape automata.

Speaker biography

Timo Jolivet is a postdoctoral researcher at the Institut de Mathématiques de Toulouse at Université Paul Sabatier, funded by LabEx CIMI.  He defended his PhD thesis in November 2013, under the co-supervision of Valérie Berthé (Université Paris Diderot, France) and Jarkko Kari (University of Turku, Finland).  During the spring of 2014, he visited Montanuniversität Leoben and TU Graz (Austria).



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