Flows on the torus
In this talk, I'll present some of the contents of two separate joint works about flows. First, joint with Andrew Marks, we produce real valued flows between sets whose boundaries have small box dimension which are simpler than the ones from our Borel circle squaring paper. Second, joint with Anton Bernshteyn and Anush Tserunyan, we produce a whole family of flows with different prescribed combinatorial properties. Further we show that our method applies to a class of functions that includes both differences of characteristic functions of sets with small boundary and Holder continuous functions with mean 0.