DubTop Seminar: Topological Structures in Derived Algebraic Geometry

In the past decade, several major advances in p-adic cohomology theory have ushered in a multitude of new questions and applications across homotopy theory, number theory, and algebraic geometry (extending even to birational geometry). At the heart of these developments is an elegant derived approach which has been essential for the discovery of new unifying theories. In this talk, I will give a survey of the language and objects involved in this beautiful story with a view toward the Hochschild-Kostant-Rosenberg theorem, a deep result connecting homotopy theory and de Rham cohomology.