Course: Computational Topology

Time: Thursday, 9:40-12:05

Location: Mondi I, Main Building, IST Austria

Instructors: Paul Bendich and Herbert Edelsbrunner

Course Description

Date Topics Assignments Lecture Notes
7.10.2010 Intro, Motivating Examples

14.10.2010 Point-Set Topology
Lecture Notes
21.10.2010 Surfaces HW #1
28.10.2010 Simplicial Complexes, Nerve Theorem

04.11.2010 Point Cloud Triangulations and the Nerve Theorem HW #2 Lecture Notes
11.11.2010 Simplicial Homology and Matrix Reduction
Lecture Notes
18.11.2010 Singular Homology, Functoriality, and Relative Homology HW #3 Lecture Notes
25.11.2010 Exact Sequences
Lecture Notes
02.12.2010 Persistence: Simplicial Context, Algorithm

09.12.2010 Persistence: Morse functions, Distance functions, Diagrams, Stability

16.12.2010 Extended Persistence and Interlevel Set Combinatorics

13.01.2011 Cohomology, Dualities

20.01.2011 Protein Docking

27.01.2011 Length of Curves

03.02.2011 Root Architecture

Main Text: Herbert Edelsbrunner and John Harer. Computational Topology: An Introduction. American Mathematical Society, 2010.

Other Articles/Books: TBA