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.
Slides: Historical background, point sets in Euclidean space, cut and project sets, crystallographic restriction, and constructing lattices and cut and project sets with prescribed rotational symmetries pdf
Slides: Review of fourier analysis, measures, tempered distributions pdf
Slides: Dynamical encoding of patches, LR classification for cubical cut and project sets, discussion of canonical cut and project sets, and examples pdf
Summary of results from Galois theory (without proofs), based on a course taught at the University of York in Fall 2014.
Review of rings and fields, pdf
Polynomial rings and irreducibility, pdf,
Field extensions and finite fields, pdf
Constructibility and Galois theory, pdf
Introduction to tiling spaces and cut and project sets
Handout for workshop at 18th Galway Topology Colloquium, June 2015
Tiling spaces and cut and project sets, pdf
Constructibility, solvability, and origami
Slides from a public lecture given for the York University Math Society
Slides from lecture, pdf
Video of lecture is available here
Topology of tiling spaces
Lectures given by Lorenzo Sadun
at the University of York in April 2014.
Lecture 1, pdf
Handout 1, pdf
Lecture 2, pdf
Handout 2, pdf
Link to Lorenzo's paper on PE cohomology
Lecture 3, pdf
Handout 3, pdf
Lecture 4, pdf
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
A reading course held at the University of Bristol in Fall 2012.
Review of measure theory, Sara Munday, pdf
Hausdorff measure and dimension, Adam Morgan, pdf
Review of point-set topology, Alan Haynes, pdf
Properties of topological groups and Haar measure, Efthymios Sofos, pdf
p-adic numbers, Martin Hauge pdf
Adeles and ideles, Matthew Palmer, pdf
Characters and the Fourier inversion formula, Daniel El-Baz, pdf
Pontryagin duality, Samuel Chow, pdf
An application to ergodic theory, Christopher White, pdf
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