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Explore a comprehensive lecture on Donaldson-Thomas and Gromov-Witten theories delivered by Artan Sheshmani at the University of Miami. Delve into the fascinating world of moduli spaces of algebraic curves and coherent sheaves, examining their induced invariants over ambient complex Kähler varieties of dimensions 2, 3, and higher. Discover why these topics have been a central focus for mathematicians over the past 50 years, uncovering their profound connections to geometry, topology, number theory, and their valuable contributions to superstring theory. Gain insights into the computation of Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties in this 1-hour and 19-minute presentation, which forms part of a broader series on these advanced mathematical concepts.