Explore the fascinating world of moduli spaces of algebraic curves and coherent sheaves in this comprehensive lecture by Dr. Artan Sheshmani from the University of Miami. Delve into the study of these mathematical structures and their induced invariants over ambient complex dimensions 2, 3, and higher, which have been a central focus for mathematicians in the past 50 years due to their relevance in superstring theory. Learn about the computation of Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties, gaining valuable insights into these important mathematical concepts. This 1-hour and 31-minute talk serves as an excellent introduction to these topics, providing a solid foundation for further exploration in the field of algebraic geometry and its applications in theoretical physics.