| | | Professor Jarkko Kari
~ Low complexity colourings of the two-dimensional grid ~
One method of deriving an aperiodic tiling, when there is no global view of how the tiles should fit together, is to have local matching rules that force the aperiodic structure to then emerge. Jarkko Kari has been interested in such local rules but from the complementary point of view of forcing a structure to become, not aperiodic, but periodic. The essential idea is that if we have a sufficiently low number of local patterns they force the overall structure to be periodic. He has been chipping away at this research area for many years, making incremental progress with difficult ideas. A video of his talk is available and it is based on a paper Jarkko co-authored with Michael Szabados in 2020; An algebraic Geometric Approach to Nivat's Conjecture.
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