College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

Let T:X to X be a homeomorphism of a Cantor space X. A speed up of T is a homeomorphism S:X to X, for which for all x in X, S(x) = T^p(x)(x) where p(x) is a positive integer. In this talk we will compare and contrast characterization theorems for speed-ups with the Giordano-Putnam-Skau characterization theorems for orbit equivalence, and also compare with measure-theoretic results. Our speedup characterization theorems will involve an epimorphism of unital ordered groups with a special condition which we call exhaustive. The exhaustive property remains a bit mysterious to me and I plan to discuss some open questions related to it. Further, unlike the case for orbit equivalence, the case where the jump function p(x) is bounded is not trivial for speedups. I will discuss some results and open questions along these lines as well.

**UICapture link to recordings:**