# Seminar 11.6.14 Rosenblatt

Speaker: Joe Rosenblatt (IUPUI)

Title: Coboundaries

Abstract: A coboundary is a difference $H – H \circ \tau$.  The function $H$ is the transfer function.   It is well-known that for ergodic transformations, a mean-zero function can be approximated by coboundaries.  How well one can do this is constrained mostly by bounds on the norm of the transfer function.   Similarly, even ergodic maps have almost invariant functions, with the primary constraint being the degree of almost invariance and how long the almost invariance should last.  These two issues are related to the ongoing effort to construct (many) pairs of maps without common coboundaries