Tom Bridgeland (University of Sheffield); October 27, 2022

Our general aim is to use the Donaldson-Thomas invariants of a 3-Calabi-Yau triangulated category to define a geometric structure on its space of stability conditions. So far we only understand how to do this in a few classes of examples. In the talk I'll explain (i) the geometry we expect to obtain (which involves a hyperkahler structure), and (ii) a moduli-theoretic construction of this geometry in the case of "categories of class S[A_1]" (where the stability space parameterises algebraic curves equipped with quadratic differentials).

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