The Expected Length of Euclidean Minimum Spanning Trees and Chromatic Persistence Diagrams

Explore the mathematical analysis of Euclidean minimum spanning trees and chromatic persistence diagrams in this 49-minute conference talk. Delve into the classic problem of determining the asymptotic constant for the expected length of Euclidean minimum spanning trees constructed from randomly sampled points, where the speaker presents improved lower bounds from 0.6008 to 0.6289 for the constant c in the relationship between expected tree length and the square root of the number of points. Examine the connection between this geometric optimization problem and the stochastic analysis of chromatic persistence diagrams, particularly focusing on the 6-pack of randomly 2-colored point sets in the unit square. Learn about the inclusion relationships between sublevel sets of monochromatic distance functions and bichromatic distance functions, and discover how similar asymptotic constants emerge in the expected 1-norms of persistence diagrams. Gain insights into collaborative research combining computational topology, probability theory, and geometric analysis through work conducted with Ondrej Draganov, Sophie Rosenmeier, and Morteza Saghafian.