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Explore the ninth installment of a lecture series on Donaldson-Thomas and Gromov-Witten theories presented by Dr. Artan Sheshmani at the University of Miami. Delve into the study 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 the profound connections these topics have to geometry, topology, number theory, and superstring theory. Learn about the computation methods for Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties in this 1-hour and 19-minute lecture, which continues the exploration of these central mathematical concepts that have captivated researchers for the past 50 years.