Title: K-Theory of Adic SpacesAbstract: We will explain a new approach to the K-theory of analytic adic spaces via condensed mathematics. Its main advantage is that it allows us to define K-theory in that context as the (continuous) K-theory of a certain dualizable stable infty-category associated to an analytic adic space (as opposed to previous […]

Title: Stone duality between condensed mathematics and algebraic geometry Abstract: One classical incarnation of Stone duality is an anti-equivalence between the categories of profinite sets and Boolean algebras respectively. In this talk, we will discuss how this can be extended to a fully faithful embedding of condensed sets into fpqc sheaves over any base field. […]