Topological data analysis

Complexes built from point clouds, persistent homology, and Mapper.

Vietoris’s complex of a point cloud (1927)

Vietoris's complex of a point cloud (1927)

Čech complexes and the nerve theorem (1932-1948)

Čech complexes and the nerve theorem (1932-1948)

Persistent homology (Edelsbrunner, Letscher and Zomorodian 2002)

Persistent homology (Edelsbrunner, Letscher and Zomorodian 2002)

Stability of persistence diagrams (Cohen-Steiner, Edelsbrunner and Harer 2007)

Stability of persistence diagrams (Cohen-Steiner, Edelsbrunner and Harer 2007)

Mapper (Singh, Mémoli and Carlsson 2007)

Mapper (Singh, Mémoli and Carlsson 2007)