Harder-Narasimhan filtrations for quiver representations from the point of view of TDA

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• Ulrike Tillmann (Isaac Newton Institute)
• Thursday 20 June 2024, 09:30-10:30
• External.

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TRHW02 - International Conference

The Harder-Narasimhan type of a quiver representation is a discrete invariant parameterised by a real-valued function (called a central charge) defined on the vertices of the quiver. We investigate the strength and limitations of Harder-Narasimhan types for several families of quiver representations which arise in the study of persistence modules. In particular, we introduce the skyscraper invariant, which amalgamates the HN types along central charges supported at single vertices, and generalise the rank invariant and generalised rank invariant studied for multiparameter persistence modules to arbitrary quiver representations.  (This is joint work with Marc Fersztand, Emile Jacquard, Vidit Nanda.)

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

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