Research Seminar: Condensed Mathematics

In this seminar we will study Clausen and Scholze’s new theory of “Condensed Mathematics”, following Scholze’s lecture notes. The language of condensed mathematics was invented in order to build a nicer framework for analytic geometry, one which unifies both the geometry of complex analytic spaces and the $p$-adic theories of rigid/Berkovich/adic spaces. We will focus on learning the theory of condensed sets/abelian groups/rings, and as an application we will see at the end how to use this to prove coherent duality for schemes.

Program: pdf.