Applied Topology Blog
Combinatorics and More (Gil Kalai's blog)
Gowers's Weblog (Timothy Gowers' blog)
Mathematical Field Notes (Johnny Evans' blog)
n-Category Café
Symplectic Field Theorist (Chris Wendl's blog)
What's New (Terrence Tao's blog)
(CIMAT Guanajuato) Applied Geometry and Topology Group
(CMU) Topological Statistics Group
(Duke) Machine Learning Group
(EPFL) Applied Topology Seminar
(INRIA) Datashape Group (formerly Geometrica)
(LBNL) Data Analysis and Visualization Group
(Michigan State) Computational Mathematics, Science, and Engineering Department
(Ohio State) Topology, Geometry, and Data Analysis Group
(Penn) Applied Topology Seminar
(Queen Mary) Applied Algebraic Topology Seminar
(Stanford) Applied Topology Blog
Applied Algebraic Topology Research Network
CHomP (Computational Homology Project)
UK Centre for Topological Data Analysis
TOPDRIM (EU Project) (no longer active)
CGAL (Computational Geometry Algorithms Library)
CHOMP Topology Software (Rutgers)
Dionysus
JavaPlex
Perseus
PHAT (Persistent Homology Algorithm Toolbox)
Ripser
Sage
Julia