BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mike Whittaker (Glasgow) DTSTART:20200604T100000Z DTEND:20200604T110000Z DTSTAMP:20260419T055843Z UID:CRMDS/4 DESCRIPTION:Title: Ap eriodic tilings: from the Domino problem to aperiodic monotiles\nby Mi ke Whittaker (Glasgow) as part of Western Sydney University Abend Seminars \n\n\nAbstract\nAlmost 60 years ago\, Hao Wang posed the Domino Problem: i s there an algorithm that determines whether a given set of square prototi les\, with specified matching rules\, can tile the plane? Robert Berger pr oved the undecidability of the Domino Problem by producing a set of 20\,42 6 prototiles that tile the plane\, but any such tiling is nonperiodic (lac ks any translational symmetry). This remarkable discovery began the search for other (not necessarily square) aperiodic prototile sets\, a finite co llection of prototiles that tile the plane but only nonperiodically. In th e 1970s\, Roger Penrose reduced this number to two. Penrose's discovery le d to the planar einstein (one-stone) problem: is there a single aperiodic prototile? In a crowning achievement of tiling theory\, the existence of a n aperiodic monotile was resolved almost a decade ago by Joshua Socolar an d Joan Taylor. My talk will be somewhat expository\, and culminate in both a new direction in aperiodic tiling theory and a new aperiodic monotile.\ n LOCATION:https://researchseminars.org/talk/CRMDS/4/ END:VEVENT END:VCALENDAR