BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART:20211004T210000Z
DTEND:20211004T220000Z
DTSTAMP:20260423T005701Z
UID:OARS/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/26/">Th
 e structure of translational tilings</a>\nby Terence Tao (UCLA) as part of
  OARS Online Analysis Research Seminar\n\n\nAbstract\nLet $F$ be a finite 
 subset of an additive group $G$\, and let $E$ be a subset of $G$.  A (tran
 slational) tiling of $E$ by $F$ is a partition of $E$ into disjoint transl
 ates $a+F\, a \\in A$ of $F$.  The periodic tiling conjecture asserts that
  if a periodic subset $E$ of $G$ can be tiled by $F$\, then it can in fact
  be tiled periodically\; among other things\, this implies that the questi
 on of whether $E$ is tileable by $F$ at all is logically (or algorithmical
 ly) decidable.  This conjecture was established in the two-dimensional cas
 e $G = {\\bf Z}^2$ by Bhattacharya by ergodic theory methods\; we present 
 a new and more quantitative proof of this fact\, based on a new structural
  theorem for translational tilings.  On the other hand\, we show that for 
 higher dimensional groups the periodic tiling conjecture can fail if one u
 ses two tiles $F_1\,F_2$ instead of one\; indeed\, the tiling problem can 
 now become undecidable.  This is established by developing a "tiling langu
 age" that can encode arbitrary Turing machines.\n\nThis is joint work with
  Rachel Greenfeld.\n
LOCATION:https://researchseminars.org/talk/OARS/26/
END:VEVENT
END:VCALENDAR