Abstract:
Prismatic cohomology was discovered by Bhatt-Morrow-Scholze as new cohomology theory of rings, closely related to TP and topological cyclic homology. Contrary to those spectrum-valued constructions, it is an "ordinary" cohomology theory and can be discussed in terms of chain complexes and sheaf cohomology. In these talks, I want to explain where this theory comes from, what structure it carries, how to think about algebraically, and how to compute with it.