Quiver moduli and quantized Donaldson-Thomas type invariants

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The central aims of the project are the explicit computation of quantized Donaldson- Thomas type invariants for quivers with stability and superpotential, the continuation of the categorification programme of M. Kontsevich and Y. Soibelman for quantized Donaldson-Thomas type invariants in terms of Cohomological Hall algebras, the exploration of the relation between quantized Donaldson- Thomas type invariants and (refinements of) Kac polynomials with a view towards the Kac conjecture, and the geometrization of the GW/Kronecker correspondence between Gromov-Witten invariants of toric surfaces and DT type invariants of quivers.