Geometry MMA Seminar: Van der Corput's Difference Theorem and the left regular representation
Sep 11, 2023, 10:30 - 11:30 AM
Speaker: Sohail Farhangi, University of Adam Mickiewicz
Title: Van der Corput's Difference Theorem and the left regular representation
Abstract: Van der Corput's Difference Theorem (vdCDT) is a useful tool in the study of multiple ergodic averages. We will begin by reviewing statements and applications of various forms of vdCDT. We will then discuss the classical Furstenberg Correspondence principle, which establishes a bridge between ergodic theory and combinatorics. Next we will show how the classical vdCDT produces sequences that have Lebesgue spectrum in a suitably interpreted sense, and that an analogous vdCDT for countable amenable groups produces sequences that correspond to subrepresentations of the left regular representation. If time permits, we will show applications by obtaining results about multiple ergodic averages for actions of countable abelian groups with noncommuting transformations.
Time: Monday, September 11 – 10:30am-11:30am
Place: Exploratory Hall, Room 4106