This will be a whirlwind tour of the mathematical field of aperiodic tilings (such as the 'Penrose' tiling). We will cover their genesis in the famous 'Hilbert problems' posed at the beginning of the 20th century, and show how these tilings connect to Turing Machines and the halting problem. This talk will end with a summary of the 'einstein' or 'one tile' problem- the search for a single tile design which can cover the entire plane, but only in a nonperiodic way.
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Hilbert, Turing and the 'einstein' problem
David Fletcher obtained a PhD in the mathematics of aperiodic tilings, from Leicester University (with MMath from Warwick). He has recently changed focus slightly, and is rapidly specializing in machine learning and data. This involved working for Tesco on optimizing store trials and predicting food promotion sales, and is now in a SaaS company collecting and analyzing data from retail fridges to help drive sales (Elstat/Nexo).