Asymptotic pairs (or, modulo shift action: asymptotic classes) are important objects in symbolic dynamics. In this talk, we discuss them in the context of Toeplitz subshifts. While Toeplitz subshifts in general allow an infinite number of asymptotic classes, we can in that case still ask if there is at least a factor (over the same odometer) with only finitely many of them. I'll present some results and partial answers to that question, from ongoing joint work with Franziska Sieron.
Contact: Daniel Lenz