Explore the theory of compact complex surfaces with p_g=q=0 in this comprehensive lecture by Kyoung-Seog Lee from the University of Miami/IMSA. Delve into the historical significance and recent developments in this active area of research. Examine the crucial role these surfaces play in complex surface theory. Gain insights into various aspects of these surfaces through the lenses of birational geometry, derived category, and gauge theory. Discover how these different mathematical approaches contribute to a deeper understanding of complex surfaces with p_g=q=0.