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Description

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.