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Hall algebras techniques for DT theory

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Severin Charbonnier
Gaetan Borot, Severin Charbonnier, Alessandro Giacchetto, Reinier Kramer and Campbell Wheeler
Fri, 24/04/2020 - 16:00 - 17:30

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Categorical statements, such as existence and uniqueness of Harder-Narasimhan filtration, can be turned into algebraic relations via Hall algebras.
The integration map then translates those relations into identities involving generating functions. This strategy is used to obtain relations on DT invariants.
We first briefly discuss the physical meaning of DT invariants. Then, following Bridgeland's survey "Hall algebras and Donaldson-Thomas invariants", we show how to employ the preceeding strategy on the quotient identity and the wall-crossing phenomenon, first with the toy example of finitary Hall algebras, second with the more realistic motivic Hall algebra.


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