Explore the intricacies of moduli spaces of algebraic curves and coherent sheaves in this 1-hour 12-minute lecture by 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. Gain insights into the computation of Gromov-Witten and Donaldson-Thomas invariants of complex algebraic varieties, as the speaker introduces these topics and provides in-depth discussions on their applications and significance in modern mathematics and theoretical physics.