Subshifts of finite type on amenable Baumslag-Solitar groups

08.06.2021 15:00 - 17:00

Nathalie Aubrun (Paris-Saclay)

Introductory talk: Wang’s tilings and the Domino problem

Abstract: Wang tiles are unit squares with colored edges. They can be assembled into a tiling of the plane iff two adjacent Wang tiles wear the same color on their common edge.This tiling model was defined in the 60’s by Hao Wang, in order to study some fragment of monadic second order logics. The Domino problem asks whether there exists or not an algorithm that takes as input a finite number of Wang tiles and outputs YES if there exists a valid tiling of the plane, and NO otherwise. In this talk I will explain the links between the decidability of the Domino problem and the existence of aperiodic Wang tile sets. We will also briefly review known results about the Domino problem generalized to other structures than the infinite grid (here Cayley graphs of groups).


Research talk: Subshifts of finite type on amenable Baumslag-Solitar groups

Abstract: Amenable Baumslag-Solitar groups are two generators one relator groups with presentation $\langle a,t | at=ta^n \rangle$ with $n$  a positive integer. In the first part of this talk I will present in details these groups and their Cayley graph, and how to embed them in $\mathbb{R}^2$. I will then review recent results about subshifts of finite type (SFTs) on amenable Baumslag-Solitar groups: indecidability of the emptiness problem for SFTs and existence of aperiodic SFTs. Based on joint works with Jarkko Kari and with Michael Schraudner.



G. Arzhantseva, A. Evetts
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