I read the title of this paper and thought to myself, “What are the chances this could be Erik Demaine?”. And sure enough!

The author gave a talk on this at Tufts during the FWCG last week. Fascinating talk.

One interesting question from audience was whether the ratio between the largest polygon piece and the smallest piece can be made bounded, as the current construction has unbounded ratio.

That's reminicient of the post correspondence problem. Is the PCP still undecidable for sets of three strings?

While not proven, is the intuition that this will also be undecideable for 1 and 2 polygon tilings?

First you ask how the hell someone could come up with this construction.

Then you realize it was this guy: https://en.wikipedia.org/wiki/Erik_Demaine