There are applications of homology theory both to Topological Data Analysis and other parts of Applied Topology (work of Gunnar Carlson and his coworkers in Stanford), via the CHOMP project to the structure of material, dynamics of Evolution of Pattern Complexity during Phase Separation etc. (The Stanford webpage mentions many more applications and they really merit a mention but I leave the 'reader' the joy of browsing around the links there.) There is also work by Robert Ghrist again on Applied Topology.
Tim Porter
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