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SUMMARY:Alexandra Kjuchukova\,"Rep-tiles"
DTSTART:20250527T120000Z
DTEND:20250527T130000Z
DTSTAMP:20260507T164000Z
UID:indico-event-13984@indico.math.cnrs.fr
DESCRIPTION:An n-dimensional rep-tile X is a compact codimension-zero subm
 anifold of R^n which has the property that it be decomposed as the union o
 f mutually isometric manifolds similar to X which have non-overlapping int
 eriors. A trivial example is the unit n-cube\, which can be written as the
  union of 2^n cubes the side length one half. More surprisingly\, all knot
  exteriors in S^3 are homeomorphic to rep-tiles\, by a 2021 result of Blai
 r\, Marley and Richards. First I will show how to construct new rep-tiles 
 with interesting algebraic topology. Then I will give an isotopy classific
 ation of rep-tiles in all dimensions. Time permitting\, I will either outl
 ine the main proof or explain the key idea\, which is a technique we calle
 d an equivariant ball swap. This is based on joint work with Ryan Blair\, 
 Patricia Cahn and Hannah Schwartz (arxiv 2412.19986).\n\nhttps://indico.ma
 th.cnrs.fr/event/13984/
URL:https://indico.math.cnrs.fr/event/13984/
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