Title: Lacunary discrete spherical averages.
Abstract: Motivated by work of Calderon and Coifman--Weiss on lacunary (continuous) spherical averages, we investigate lacunary discrete spherical averages of Magyar--Stein--Wainger. This turns out to be surprisingly different from the Euclidean case. We discover a new connection to ergodic theory and discuss a p-adic Seeger--Wainger--Wright theorem. This is joint work with Jim Wright and Jacek Zienkiewicz.