Explore the advanced mathematical concepts of Donaldson-Thomas and Gromov-Witten theories in this 1-hour 24-minute lecture delivered 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 dimensions 2, 3, and higher. Gain insights into these topics that have been a central focus for mathematicians over the past 50 years 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 sophisticated mathematical theories and their applications.