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Explore the advanced mathematical concepts of Donaldson-Thomas and Gromov-Witten theories in this 1-hour 21-minute lecture by Artan Sheshmani from the University of Miami. Delve into the study of moduli spaces of algebraic curves and coherent sheaves, and their induced invariants over ambient complex dimensions 2, 3, and higher. Gain insights into these topics that have been a central focus for mathematicians in the past 50 years due to their relevance in superstring theory. Learn about the computations of Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties, providing a deeper understanding of these fundamental concepts in algebraic geometry and mathematical physics.