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Explore a mathematical research seminar where Mr. Marc Fersztand from the University of Oxford delves into the Harder-Narasimhan filtrations of persistence modules, examining the strength and limitations of Harder-Narasimhan types in Topological Data Analysis. Learn about the skyscraper invariant, which combines HN types along central charges at single vertices, and discover how it surpasses the rank invariant in effectiveness. Understand the conditions under which the HN type serves as a complete invariant for various families of persistence modules, based on joint research with Emile Jacquard, Vidit Nanda, and Ulrike Tillmann. Delivered at the Isaac Newton Institute as part of the EMG (New equivariant methods in algebraic and differential geometry) event series, this presentation offers insights into advanced mathematical concepts at the intersection of algebraic geometry and data analysis.
