Abstract:
Many questions in dynamics are reduced to questions about the cocycles. Of particular interest is to know when a cocycle is a coboundary. I will make a comparative study of the cocycle properties for measurable dynamics, topological dynamics, Cantor dynamics and Borel dynamics.  I will discuss versions of the classical Gottschalk Hedlund theorem. If time permit, I will also talk about versions of Rokhlin lemma, in topological and Borel dynamics.