Lecture by Thierry Monteil (U. Paris XIII) at IPM, Tomorrow 2pm.

[Meysam Nassiri]

TITLE:

Quantifying the Aperiodicity of a Wang Tile Set.

SPEAKER:

Thierry Monteil (Université Paris 13, France)

TIME:

Tuesday, November 27, 2018, 14:00 - 15:00

VENUE:

Lecture Hall 1, Niavaran Bldg.

SUMMARY:

A (Wang) tile set is a finite set of unit squares where each edge got a color. A tile set T tiles the plane if the plane can be covered by Z^2-translated copies of elements of T, where two adjacent edges must have the same color. A tile set is aperiodic if it tiles the plane, but if this can not be done in a periodic way. Most aperiodic tilings are obtained from a substitution process (Penrose, Ammann-Beenker, Robinson,...). We will introduce two invariants to quantify the level of aperiodicity of a Wang tile set. The first one is topological, the second is metric. They both rely on the way a tile set tile can tile other objects than the plane, namely translation surfaces and cylinders. The second invariant allows us to prove that the tile sets of Kari and Culik are not ruled by a substitution process.

URL: http://math.ipm.ac.ir/seminars/printseminar.jsp?eventID=330