General course info
- Neža Mramor Kosta (firstname.lastname@example.org)
- Žiga Virk (email@example.com)
- Aleksandra Franc (firstname.lastname@example.org)
- Gregor Jerše (email@example.com)
Introduction. Basic definitions and concepts: metrics, continuous maps, homeomorphisms, homotopy type.
Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic
Simplicial complexes on data sets:
Levenshtein distance calculator:
Interleaving. Algebraic groups. Intuition and idea of homology.
A nice explanation of the algorithm to compute homology:
You can also use Dionysus to compute homology (and much more):
Wolfram Demonstration of computing simplicial homology of an alpha complex:
Homology with Sage:
Homology (and more) with CHomP:
Persistent homology: bar codes, persistence diagrams
Discrete Morse theory: discrete Morse functions, discrete gradient vector fields, Morse chain complex and Morse homology
No school this week:)
Happy New Year!!