Workshop: Multiple ergodic averages with Möbius weight, Joni Teräväinen

Speaker
Joni Teräväinen, University of Turku

Abstract
Motivated in particular by Furstenberg’s proof of Szemerédi’s theorem and its polynomial generalisation by Bergelson and Leibman, multiple ergodic averages have been studied actively in recent decades. The problem of their pointwise convergence nevertheless remains open. I will first introduce these multiple ergodic averages and review progress made on their convergence properties. I will then discuss a result on the pointwise convergence of multiple ergodic averages weighted by the Möbius function, which goes beyond what is currently known about the unweighted case and answers a question of Frantzikinakis.