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Explore a comprehensive lecture on Donaldson-Thomas and Gromov-Witten theories in this nearly two-hour presentation by Dr. Artan Sheshmani from 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 dimensions 2, 3, and higher. Gain insight into why these topics have captivated mathematicians for the past 50 years, particularly due to their relevance in superstring theory. Learn about the computation methods for Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties, enhancing your understanding of these crucial mathematical concepts.