This is a 10-days school of mathematics & theoretical computer science for students from Iran and neighbor countries. It is devoted to mathematical aspects of tilings in the various contexts where they appear, with an effort to achieve coherence of the program:
- discrete geometry (models of discrete surfaces),
- computability (local constraints on the way tiles can fit model transportation of information, similarly to the local rules of cellular automata),
- probability (convergence of stochastic processes on tilings, in particular random sampling, and typical properties of random tilings),
- combinatorics (counting the number of ways a region can be tiled),
- symbolic dynamics (coding trajectories of minimal non-periodic dynamical systems),
- effective algebraic geometry (use of Groebner basis to check tileability of a region or existence of a characterization by local patterns).
In addition to these “classical” themes, there will be satellite lectures related to the rich historical heritage of Isfahan (and more generally the islamic world), where tilings with quasicrystalline symmetries can often be found on architectural buildings. The Isfahan Mathematics House has already organized workshops on such thematics.