Bounded remainder sets for rotations on the adelic torus (part 1/2)
April 16, 2018
1:00 pm PHG 646
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 these talks 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.
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