Diophantine Approximation – How to approximate complicated numbers by simple fractions

PhD defence, Wednesday 11 October 2017, Morten Hein Tiljeset.

2017.10.11 | Steffi Hjerrild Iversen

Morten Hein Tiljeset

Diophantine Approximation concerns the problem of approximating numbers by simple fractions. A classic example is the number pi = 3.1415..., where the decimal expansion continued infinitely. This number can be approximated by the fraction 22/7 with an error of just above 0.04%. Aside from making calculations easier, many phenomena can in practice only be described by simple fractions. The ratio produced by a gear train is the ratio of the number of teeth on the gear wheels. A more complicated fraction is thus more expensive to produce. The theory also describes why a piano has 12 keys per octave: This minimizes the error from the correct tone (other good choices are 5, 41, 53 and 306 keys per octave).

In his research, MSc Morten Hein Tiljeset has studied the more general question of how to approximate points on certain geometric objects such as circles and spheres. One of the motivations for this work, is to choose a finite set of rotations in three dimensions, which in an optimal way can approximate an arbitrary rotation. This problem is related to the theoretical construction of efficient quantum computers.

The PhD degree was completed at the Department of Mathematics, Faculty of Science and Technology, Aarhus University.

This résumé was prepared by the PhD student.

Time: Wednesday 11 October 2017 at 12.15
Place: Lecture theatre D1 (1531-113)
Title of dissertation: Intrinsic Diophantine Approximation
Contact information: : Morten Hein Tiljeset, e-mail: morten@tiljeset.com, phone.: 61 71 24 97
Members of the assessment committee:
Professor Timothy Daniel Browning, School of Mathematics, University of Bristol, UK
Senior Lecturer Detta Dickinson, Department of Mathematics and Statistics, National University of Ireland Maynooth
Professor Bent Ørsted, Department of Mathematics, Aarhus University
Main supervisor:
Associate Professor Simon Kristensen, Department of Mathematics, Aarhus Universitet
Language: The PhD dissertation will be defended in English

The defence is public.
The dissertation is available for reading at the Graduate School of Science and Technology/GSST,
Ny Munkegade 120, building 1520, rooms 128-134, 8000 Aarhus C.

PhD defence
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Revised 23.02.2018