Written via top specialists, this ebook explores numerous instructions of present study on the interface among dynamics and analytic quantity conception. themes comprise Diophantine approximation, exponential sums, Ramsey concept, ergodic conception and homogeneous dynamics. The origins of this fabric lie within the 'Dynamics and Analytic quantity idea' Easter university held at Durham college in 2014. Key options, state of the art effects, and sleek innovations that play a necessary position in modern study are offered in a way obtainable to younger researchers, together with PhD scholars. This ebook can be valuable for proven mathematicians. The parts mentioned comprise ubiquitous structures and Cantor-type units in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, a number of recurrence and Ramsey thought, counting and equidistribution difficulties in homogeneous dynamics, and purposes of skinny teams in quantity conception. either dynamical and 'classical' techniques in the direction of quantity theoretical difficulties also are supplied.
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