Speaker: Katharine Turner (Australian National University)
Title: Algebraic Wasserstein distance between persistence modules
Abstract: It is now well understood that the interleaving distance between persistence modules is the same as the bottleneck distance between their corresponding persistence diagrams. A common choice of metric for between persistence diagrams is the p-Wasserstein distance - where the bottleneck distance is the limit as p goes to infinity. In this talk I shall present an algebraic version of p-Wasserstein distance which is defined for persistence modules and agrees with the p-Wasserstein distance for their corresponding persistence diagrams. I will also discuss new stability results for these Wasserstein distances. The work presented was in collaboration with Primoz Skraba.
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