Explore the intricacies of the planar stochastic heat equation and the directed landscape in this 43-minute Toronto Probability Seminar talk by Balint Virag from the University of Toronto. Delve into the fundamental concepts of the directed landscape, examining what factors are significant and which can be disregarded. Gain insights into various models and learn the process of solving the stochastic heat equation. Investigate the weak ordered heat equation, stochastic integration, and the KPZ equation. Analyze limits and direct definitions before concluding with a general overview and technical details. This seminar, presented at the Fields Institute, offers a comprehensive exploration of advanced probability concepts for mathematicians and researchers in related fields.