Convex geometry for (co)fans of abelian categories

Abstract: Arising in cluster theory, the g-vector fan is a convex geometric invariant encoding the mutation behaviour of clusters. In representation theory, the g-vector fan encodes the mutation theory of support tau-tilting objects or, equivalently, two-term silting objects. In this talk, we will describe a generalisation of the g-vector fan which in some sense “completes” the g-vector fan: the heart fan of an abelian category. This convex geometric invariant encodes many important homological properties: e.g. one can detect from the convex geometry whether an abelian category is length, whether it has finitely many torsion pairs, and whether a given Happel-Reiten-Smaloe tilt is length. This talk will be a report on joint work with Nathan Broomhead, David Ploog and Jon Woolf.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

K-theory and homologyquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Paris algebra seminar

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