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A colloquium on discrete curvature

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Gromov-Wasserstein distances and lower bound

Facundo Memoli

I will describe the construction of the GW metric, its properties, and discuss how the representation of datasets as metric measure spaces gives rise to a number of stable invariants which are counterparts to concepts emerging in topology and differential geometry, including analogues to homology and notions of curvature that are valid beyond the smooth case.