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Multiparameter persistent homology is a generalization of ordinary
persistent homology which arises naturally in the study of noisy point
cloud data.  It yields algebraic invariants of data called persistence
modules, which can be far more complex than the barcode invariants provided
by ordinary persistent homology.  As such, adapting the usual persistence
methodology for TDA to the multiparameter setting requires new ideas.  One
such idea, explored in my work, is that in spite of the algebraic
complexity of multiparameter persistence modules, there is a simple and
very well behaved metric on these modules called the interleaving distance,
which generalizes the bottleneck distance commonly considered in the
1-parameter case.  Using the interleaving distance, we can begin to adapt
the many TDA results given in terms of the bottleneck distance to the
multiparameter setting.

This talk will be primarily on theoretical foundations of TDA, but if time
permits, I'll also give a brief demonstration of a software tool I have
designed with Matthew Wright for the interactive visualization of
2-parameter persistent homology.