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Learn about Delaunay bifiltrations and their topological equivalence to sublevel-offset filtrations in this 46-minute conference talk. Explore how finite point sets in Euclidean space equipped with real-valued functions lead to two-parameter filtration settings, and discover the newly introduced Delaunay and Delaunay-Cech bifiltrations that maintain topological equivalence while achieving computational efficiency with O(n^{ceil((d+1)/2)}) size complexity. Understand the practical applications in low-dimensional spaces (d = 2 or 3) and examine the adapted Bowyer-Watson algorithm for computing Delaunay triangulations in the bifiltration context. See how this approach enables computation of Delaunay-Cech bifiltrations on point clouds in R^3 with tens of thousands of points in seconds, and if time allows, explore extensions to trifiltrations based on collaborative research with Angel Alonso, Michael Kerber, and Mike Lesnick.
