Explore the advanced mathematical concepts of stack-theoretic weighted blowups and their applications in a comprehensive lecture. Delve into the efficiency and natural approach these techniques bring to algorithms like resolution of singularities and destackification. Gain insights into the intricate workings of wall-crossings and weak factorization through expert explanations and demonstrations. This hour-long presentation offers a deep dive into cutting-edge mathematical theory and its practical implications for solving complex problems in algebraic geometry.