Derived microlocal geometry and virtual invariants

We will introduce a derived geometric generalization of the microlocal sheaf theory, which gives a new perspective on virtual invariants for derived moduli spaces. As an application, we will construct a Hall algebra structure on the cohomological Donaldson-Thomas invariants for the canonical bundle of smooth algebraic surfaces, which gives a 3d refinement of the 2d cohomological Hall algebra due to Kapranov-Vasserot. This talk is based on a forthcoming joint work with Adeel Khan.

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