Matolcsi Máté: A lonely weak tile

The notion of weak tiling was a key ingredient in the proof of Fuglede's spectral set conjecture for convex bodies, due to the fact that every spectral set tiles its complement weakly with a suitable Borel measure. In this talk, we review the concept of weak tiling and answer a question raised earlier in the literature: we give an example of a set that tiles its complement weakly, but is neither spectral nor a proper tile. 

Joint work with Gergely Kiss, Itay Londner, and Gabor Somlai.