University of Birmingham > Talks@bham > Geometry and Mathematical Physics seminar > Some homological algebra behind scattering diagrams

Some homological algebra behind scattering diagrams

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If you have a question about this talk, please contact Timothy Magee.

The notion of scattering diagram arose in mirror symmetry and have shown to be a powerful tool in the study of cluster algebras, being used to prove a wide range of conjectures in the theory. Recently, Bridgeland showed that cluster scattering diagrams can be built using the representation theory of quivers using stability conditions and motivic Hall algebras. Moreover, he showed that his methods can be applied in a much more general setting, constructing a scattering diagram for every finite dimensional algebra over an algebraically closed field.

In this talk, after explaining briefly the construction by Bridgeland, I will show how the stability conditions used in his construction can be recovered by the homological properties of the module category the algebra. Time permitting, I will talk about some “toric” properties arising in the homological algebra of module categories.

Part of this work is joint with T. Brustle and D. Smith from the University of Sherbrooke.

This talk is part of the Geometry and Mathematical Physics seminar series.

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