| | | Daniel Roca González
~ Hyperuniformity of Hat tilings ~
If a large circle is placed over a tiling, then the number of tiles of the various types within the circle can be counted. Where the circle is placed may make a difference but we can calculate the mean and the variance of all possible placements of a circle of a given size. Now, if the circle is increased in size, the tiling is said to be hyper-uniform if the variance grows more slowly than the circle's area. Daniel's talk looked at this concept in various settings, culminating in the result that the Hat tiling is hyper-uniform. A video of the talk is available. A general introduction to the topic appeared in Quanta magazine in 2016.
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