TCS lab seminar:"Local rules for cut and project tilings"
Laboratory of Theoretical Computer Science will have the next seminar on Wednesday, September 20, 18:10.
The seminar will be held in HSE at 11 Pokrovsky Boulevard, building R, room R308.
For online participation:
Title: Local rules for cut and project tilings
Speaker: Thomas Fernique
Abstract: The cut-and-project method was introduced in the 1980s to define non-periodic tilings, as an alternative to the substitution method. The simplest case is that of a straight line drawn on a grid sheet: the sequence of cut horizontal or vertical segments, projected onto the line, forms a tiling of the line which is non-periodic as soon as the slope is irrational. This extends to higher dimensions (the celebrated Penrose tilings, for example, can be obtained from an algebraic plane in Euclidean space of dimension 5). The same question as for tilings defined by substitution then arises: which of these tilings do admit local rules, i.e. can be characterized only by their patterns of a given finite size? In this presentation, the cut and project method will be presented without assuming any prior knowledge. Then, some remarkable characterizations of (non-)existence of local rules will be presented and illustrated with examples as simple as possible.