Counting and combinatorics in aperiodic order

Combinatorial objects and methods naturally appear in the study of aperiodic order and mathematical quasicrystals. In the talk I will describe how aspects of matchings, graphs, counting and discrepancy can imply results on certain measures of order and disorder in long-range geometry, with applications to classical constructions such as the Penrose tiling as well as to recent developments in aperiodic order. Partially based on joint work with Yaar Solomon.