Reading List

H. Edelsbrunner and J.L. Harer, Computational Topology - An Introduction,AMS (2010).

See also, U. Tillmann, Lecture notes for CAT 2012, in http://people.maths.ox.ac.uk/tillmann/CAT.html

Topic A:

1. G. Carlsson, Topology and data, Bulletin A.M.S.46 (2009), 255-308.
2. H. Edelsbrunner, J.L. Harer, Persistent homology: A survey, Contemporary Mathematics 452 A.M.S. (2008), 257-282.
3. S. Weinberger, What is ... Persistent Homology?, Notices A.M.S. 58 (2011), 36-39.
4. P. Bubenik, J. Scott, Categorification of Persistent Homology, Discrete Comput. Geom. (2014), 600-627.

Topic B:

1. S. Abramsky and Adam Brandenburger, The Sheaf-Theoretic Structure Of Non-Locality and Contextuality. In New Journal of Physics, 13(2011), 113036, 2011.
2. S. Abramsky and L. Hardy, Logical Bell Inequalities, {Phys. Rev. A} 85, 062114 (2012).
3. S. Abramsky, S. Mansfield and R. Soares Barbosa, The Cohomology of Non-Locality and Contextuality, in Proceedings of Quantum Physics and Logic 2011, Electronic Proceedings in Theoretical Computer Science, vol. 95, pages 1-15, 2012.