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Many questions and a few answers about hom-shifts and rectangular tiling shifts in higher dimensions

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we will step back from the generality of multidimensional shifts of finite type and focus on two specific classes: The space of graph homomorphisms from $\mathbb Z^d$ to a fixed connected undirected graph and the space of tilings of $\mathbb Z^d$ by rectangular shapes. While these classes cover fairly well-studied examples like the space of proper 3-colourings and domino tilings, a lot still remains to be understood. We will discuss some recent results about these shift spaces and try to pinpoint the difficulties which arise in their investigation.

Mathematics; Dynamical systems and ergodic theory; Group theory and generalizations; Dynamical systems

video/mp4

Author affiliation: Hebrew university of Jerusalem

2019-11-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72265

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/