two-parameter persistent homology

Wednesday, August 15, 2018 - 1:00pm - 1:30pm
Roy Zhao (University of California, Berkeley)
RIVET computes degree-Rips bifiltrations, a two-parameter version of the Vietoris Rips complex that takes the density of points into account. In a Rips complex, a simplex appears when all of its faces appear. When computing single parameter persistent homology, we can simply take the maximum time of appearance of its faces to be the time of appearance of a particular simplex. However, in the two-parameter case, the picture is complicated because a simplex can appear at multiple incomparable indices.
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