Explore recent developments in algebraic geometry over p-adically complete commutative rings in this one-hour lecture by Bhargav Bhatt. Delve into topics such as Hensel's p-adic world, prismatic cohomology, semistable reduction, and connections to algebraic K-theory. Examine the shape of prismatic cohomology and its applications, including new calculations in algebraic K-theory and Kodaira vanishing in mixed characteristic. Gain insights into Serre's global-to-local dictionary and various variants and applications of Kodaira vanishing. Access accompanying slides for visual support and deeper understanding of the presented concepts.