TRHW02 | Prof. Ulrike Tillmann | Harder-Narasimhan filtrations for quiver representations

TRHW02 | Prof. Ulrike Tillmann | Harder-Narasimhan filtrations for quiver representations from the point of view of TDA
Speaker: Professor Ulrike Tillmann (Isaac Newton Institute)
Date: 20th Jun 2024 - 9:30 to 10:30
Venue: External
Title: Harder-Narasimhan filtrations for quiver representations from the point of view of TDA
Event: (TRHW02) International Conference
Abstract: 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 therank invariant and generalisedrank invariant studied for multiparameter persistence modules to arbitrary quiver representations.
(This is joint work with Marc Fersztand, Emile Jacquard, Vidit Nanda.)
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