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Tuesday, September 28
Mathematics Colloquium: Directional ergodicity and weak mixing for Z^d actions
03:35 PM - 06:00 PM
Location: Science Center Room 323

Speaker: Dr. Ayse Sahin (Wright State University)

Abstract: We study probability measure-preserving actions of Z^d and ask if the action is ergodic (weak mixing) and H<Z^d is a subgroup. Will restricting to the subgroup H necessarily give an ergodic (weak mixing) H action? More generally, we define ergodicity and weak mixing of the action in arbitrary directions that do not correspond to a subgroup of Z^d. We show that both directional ergodicity and weak mixing can be characterized in terms of the measure of the maximal spectral type of the Z^d action. Using this characterization, we prove several results establishing what freedom exists in directional behavior. We also show that if T is a weak mixing Z^d action then it is ergodic in a direction if and only if it is weak mixing in that direction.

Refreshments will be served at 3:15 PM in the conference room 313F.

This is joint work with E. Arthur Robinson and J. Rosenblatt.

Contact Information:
Name: Muhammad Usman