Lecture Notes

Diophantine approximation and aperiodic order

Lecture notes covering the following topics: background on Diophantine approximation, shift spaces and Sturmian words, point sets in Euclidean space, cut and project sets, crystallographic restriction and construction of cut and project sets with prescribed rotational symmetries, a dynamical formulations of pattern recognition in cut and project sets, a discussion of diffraction, and a proof that cut and project sets have pure point diffraction measures.

Galois theory

Summary of results from Galois theory (without proofs), based on a course taught at the University of York in Fall 2014.

Introduction to tiling spaces and cut and project sets

Handout for workshop at 18th Galway Topology Colloquium, June 2015

Constructibility, solvability, and origami

Slides from a public lecture given for the York University Math Society

Topology of tiling spaces

Lectures given by Lorenzo Sadun at the University of York in April 2014.

Impressions of Tate: A graphical approach to mixed Tate motives

Lectures given by Owen Patashnick at the University of York in January 2014.

An invitation to geometric and Diophantine Fourier analysis

Lectures given by Tuomas Sahlsten at the University of York in December 2013, based on this paper.

Topological groups

A reading course held at the University of Bristol in Fall 2012.

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