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.
  • Full lecture notes, pdf
  • 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
  • Practice problems pdf
  • Galois theory
    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.
  • Lecture 1, pdf
  • Lecture 2, pdf
  • Lecture 3, pdf
  • Lecture 4, pdf
  • 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.
  • 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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