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Harder-Narasimhan Filtrations of Persistence Modules

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EMG - New equivariant methods in algebraic and differential geometry

The Harder-Narasimhan type of a quiver representation is a family of discrete invariants parameterised by a real-valued function (called a central charge) defined on the vertices of the quiver. In this talk, we investigate the strength and limitations of Harder-Narasimhan types for several families of quiver representations which arise in Topological Data Analysis. We introduce the skyscraper invariant, which amalgamates the HN types along central charges supported at single vertices, and show that it is strictly finer than the rank invariant. We also study, for several families of persistence modules, the set of central charges for which the HN type is a complete invariant. This work is detailed in the preprint https://arxiv.org/abs/2303.16075. It is a joint work with Emile Jacquard, Vidit Nanda and Ulrike Tillmann.

This talk is part of the Isaac Newton Institute Seminar Series series.

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