Explore the intricacies of geometric and modular representation theory in this seminar talk delivered by James Tao from the Massachusetts Institute of Technology. Delve into the complex topic of the affine Hecke category as a monoidal colimit, beginning with an introduction to key theorems and motivations. Progress through definitions, nonmonoidal limits, and the Master Theorem, while gaining insights into Cartesian and geometric intuitions. Examine various applications, including special cases and general applications, before investigating generating objects and iterated extensions. Culminate with the main theorem, joint thoughts, and the key idea behind the deformation construction. Enhance your understanding of advanced mathematical concepts in this comprehensive lecture from the Institute for Advanced Study's Geometric and Modular Representation Theory Seminar series.