Mathematics Seminar
By Yihan Zhu
Thusrday, July 17, 2025, at 2:30 pm
University of Windsor | In-person | Lambton Tower 9-118
Title: Equidistribution of continuous functions between topological spaces
Abstract: Intuitively, a sequence is equidistributed in a set if every subset gets its "proportional share" of points. Defining equidistribution rigorously requires specifying precisely which subsets to consider and how proportional shares are measured. In this talk, we introduce and investigate a generalized notion of equidistribution for continuous functions between topological spaces and prove the existence of such equidistributed functions. We present a measure-theoretic characterization that provides necessary and sufficient conditions for the equidistribution of continuous functions. We investigate the notion of almost periodic equidistribution and give an analogue of Weyl's criterion for almost periodically equidistributed functions taking values in arbitrary topological groups. As an application of the generalized Weyl's criterion, we extend van der Corput's difference theorem to multidimensional sequences taking values in arbitrary topological groups. We introduce a class of Diophantine inequalities having infinitely many integer solutions along arithmetic progressions. Moreover, we discuss connections between measure-preserving maps, ergodicity, and equidistribution theory.
Counts toward seminar attendance for MSc and PhD students in Math & Stats