Explore holomorphic bisectional curvature and its applications in a 58-minute lecture by Gregory Pearlstein from Texas A&M University. Delve into the fundamental role of curvature properties in Hodge theory, focusing on recent work with Chris Peters on Hodge metrics in mixed Hodge theory. Examine rigidity results for geometric classes of examples and gain insights into topics such as the Mixture Alley Theorem, Gaussian Connection, Period Map, and deformations. Investigate the communication condition, classification space, and the analog of hot deformation, while also exploring pure cases and abstract conditions related to this complex mathematical subject.