Explore the intricacies of Donaldson-Thomas invariants in this advanced mathematics lecture. Delve into the construction of virtual fundamental classes in motivic cohomology theory for smooth projective 3-folds. Examine the development of quadratic Donaldson-Thomas invariants and their refinement using the cohomology of the sheaf of Witt rings. Discover recent developments, conjectures, and computations related to these refined invariants, including work on their signatures by Anneloes Viergever. Gain insights into complex mathematical concepts presented by Marc Levine from Universität Duisburg-Essen in this 1-hour 12-minute talk from the Institut des Hautes Etudes Scientifiques (IHES).