Equidistribution Modulo Finite Groups in Shifts

This talk from the Workshop on "Uniform Distribution of Sequences" at the Erwin Schrödinger International Institute for Mathematics and Physics explores equidistribution results with respect to finite groups for shift spaces through ergodic properties of skew products between shift spaces and finite groups. Discover the study of density of group languages (rational languages recognized by morphisms onto finite groups) within shift spaces, with specific examples like the frequency of words with an even number of a given letter. The presentation examines both shifts of finite type (with appropriate irreducibility notions) and minimal shifts, providing a closed formula for density in cases where skew products have minimal closed invariant subsets that are ergodic under the product of the original measure and uniform probability measure on the group. This 48-minute talk represents joint work with H. Goulet-Ouellet, C.-F. Nyberg-Brodda, D. Perrin and K. Petersen.