Ian Selvaggi (SISSA)
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PDL C-38
Title pretalk: A gentle introduction to Bridgeland stability conditions
Abstract pretalk: Inspired by work on String Theory, Bridgeland developed a far-reaching formalism for stability conditions on derived categories. The resulting theory has been extremely successful, with applications ranging from enumerative invariants to representation theory. I will convey the main ideas and constructions by tracing similarities with the case of slope stability for curves, highlighting the desired properties for the existence of good moduli spaces for the corresponding stacks of semistable objects.
Title: The deformation property of locally constant stability conditions
Abstract: One of the truly remarkable features of Bridgeland stability conditions, the deformation property, tells us that the set of such has a natural structure of a complex manifold. Thus, it is very interesting to see how the hypotheses which grant the existence of good moduli spaces for the stacks of semistable objects interact with the manifold structure. In this talk I will explain the more recent approach to the construction of relative moduli spaces in the noncommutative setting, due to Halpern-Leistner—Robotis, and outline how an analogue of the deformation property can be carried in this context. Notably, the conditions allowing for the existence of good moduli spaces turn out depend only on the connected components of the resulting manifold.