Diophantine Approximation, Dynamical Systems, and Phase Spaces with singularities

The event is taking part on the Tuesday, Jun 5th 2018 at 15.30
Theme/s: Applied Mathematics
Location of Event: AT 306
This event is a: Public Seminar

Abstract: In a famous paper from 1930, Hardy & Littlewood published a result in Diophantine Approximation, analysing the growth of a series of cosecants. In "The Collected Papers of GH Hardy", Davenport wrote in an introduction: "The proof of this remarkable result is curiously indirect; it involves contour integration and the use of Cesaro means of arbitrarily high order". He listed as one of the top 5 unsolved problems from Hardy's work: "The problem is to give a simpler and more direct proof of these results".

A step in this direction was made in 2009 by Sinai and Ulcigrai who proved a result on the related series of cotangents using the "cut and stack" technique of interval dynamics. Although elementary, the proof was far from simple. We will present another new approach based on circle dynamics, and the challenges remaining.

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External Speakers

Dr Paul Verschueren