Computational Algebraic Topology 2016/17


Course outline

  • Official course website
  • Lectures notes (lectures 1-6)
  • SA-Lecture1
  • SA-Lecture2
  • SA-Lecture3
  • SA-Lecture4
  • SA-Lecture5
  • SA-Lecture6
  • Exercises for week 2
  • Exercises for week 4
  • Exercises for week 6
  • Exercises for week 8

  • Resources

    Reading for the core material and Topic A:
  • Lecture notes for core material and Topic A from 2012
  • Lecture notes for the C3.1 Algebraic Topology course from 2013
  • Elementary Applied Topology by Robert Ghrist
  • What is persistent homology? by Shmuel Weinberger
  • Topology and data by Gunnar Carlsson
  • Introduction to PH Video by Matthew Wright
  • A roadmap for the computation of persistent homology
  • Categorification of persistent homology by Bubenik and Scott
  • Gromov-Hausdorff Stable Signatures for Shapes using Persistence by Chazal, Cohen-Steiner, Guibas, Memoli, and Oudot
  • Spectral sequences, exact couples andpersistent homology of filtrations by Basu and Parida
  • Discrete Morse theory for computing cellular sheaf cohomology by Curry, Ghrist, Nanda
  • Topological Pattern Recognition for Point Cloud Data by Carlsson
  • A roadmap for the computation of persistent homology by N. Otter, M. Porter, U. Tillmann, P. Grindrod, H. Harrington
  • Reading for Topic B:
  • The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
  • Contextuality, Cohomology and Paradox
  • The Cohomology of Non-Locality and Contextuality
  • Contextual Semantics: From Quantum Mechanics to Logic, Databases, Constraints, and Complexity

  • Other links

  • CAT workshop 2015
  • CAT school 2015
  • Alan Turing Institute