Chung-Ping Lai will finish his talk on cubical homology and Arthur Mills will start his talk on "Computing Homology Groups with the Smith Normal Form", see the abstract below.
Topological data analysis involves the computation of the homology groups of a space built up from data. Computing these groups poses challenges both in mathematics and programming. This introductory talk will show how the Smith normal form of an integer matrix can be used to quickly obtain the homology of a chain complex of finitely generated free abelian groups. This procedure sets the stage for computing the homology groups of cubical sets obtained from real-world data -- a topic that will be covered in a future presentation.