Representation theoretic aspects of scattering diagrams

Abstract: The notion of algebraic scattering diagram associated to any finite dimensional algebra was recently introduced by Bridgeland as an algebraic construction of the celebrated cluster scattering diagrams of Gross, Hacking, Keel and Kontsevich. In this talk, after briefly recalling the construction of scattering diagrams given by Bridgeland, we will show how the homological aspects of the module category determine several properties of the support of the scattering diagrams. In particular, we will show that chambers in the scattering diagram of an algebra are in one-to-one correspondence with certain torsion pairs in its module category. This is joint work with Thomas Brustle and David Smith. Based on this characterisation, we will discuss how the study of torsion pairs in the module category of algebras can play a key role in the calculation of Donaldson-Thomas invariants for certain Calabi-Yau threefolds.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

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