Explore a comprehensive lecture on open Donaldson-Thomas invariants presented by Sergei Gukov from Cal Tech at the University of Miami. Delve into the intricate world of invariants, moduli spaces, and generating series as the speaker proposes new approaches to understanding these mathematical concepts. Learn about refined invariance, boundary conditions, and model lifespace while examining open invariants through rhetorical analysis and practical examples. Investigate the implications of infinite projects, topological vertex, and partitions in this class of examples. Gain insights into the counting methods and the proposed framework for advancing the field of Donaldson-Thomas theory.