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Texas A&M Number Theory Seminar

Department of Mathematics
Blocker 220
Wednesdays, 1:15–2:15 PM


Alan Haynes

University of Houston

Wednesday, April 11, 2018

Blocker 220, 1:15PM

Title: Bounded remainder sets for rotations on the adelic torus

Abstract: Bounded remainder sets for a dynamical system are sets for which the Birkhoff averages of return times differ from the expected values by at most a constant amount. These sets are rare and important objects which have been studied, especially in the context of Diophantine approximation, for over 100 years. In the last few years there have been a number of results which culminated in explicit constructions of bounded remainder sets for toral rotations in any dimension, of all possible allowable volumes. In this talk we are going to explain these results, and then explain how to generalize them to give explicit constructions of bounded remainder sets for rotations on the adelic torus. Our method of proof combines ideas from harmonic analysis on the adeles, dynamical systems, and the theory of mathematical quasicrystals.