Contractibility of the space of stability conditions for silting-discrete algebras

David Pauksztello (Lancaster)

Frank Adams 1,

The space of stability conditions on a triangulated category can be considered a continuous generalisation of bounded t-structures, and therefore can be thought of as a geometric invariant encoding the homological information contained in a triangulated category. When nonempty, it is widely believed to be contractible, which would have deep consequences in algebraic geometry and mathematical physics. In this talk, I will outline the definition of stability conditions, explain work of Qiu and Woolf on how it becomes a cellular stratified topological space, and then explain how the mutation theory of bounded t-structures allows one to use the cellular stratified structure to show contractibility. This talk will be based on joint works with Nathan Broomhead, David Ploog, Manuel Saorin and Alexandra Zvonareva.

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