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Explore a comprehensive lecture on Donaldson-Thomas and Gromov-Witten invariants in this 1-hour 17-minute talk by Artan Sheshmani from the University of Miami. Delve into the fascinating world of moduli spaces of algebraic curves and coherent sheaves, and their induced invariants over ambient complex dimensions 2, 3, and higher. Discover why these topics have been a central focus for mathematicians over the past 50 years, particularly due to their relevance in superstring theory. Gain insights into the computation methods for Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties. This lecture serves as an excellent introduction to these advanced mathematical concepts, providing a solid foundation for further study in algebraic geometry and string theory.