Speaker: Catrin Mair – Technical University of Darmstadt
Abstract: The $\infty$-category $Cond(Ani)$ of condensed anima combines the homotopy theoretic direction of anima with the topological space direction of condensed sets. Hence, it is natural to ask for its role in homotopy theory. For instance, one can assign to every condensed anima a pro-homotopy type by which we can recover the “shape” of a sufficiently nice topological space. In my talk, I will focus on explaining how to define a refinement of the étale homotopy type of a scheme as an object in $Cond(Ani)$. This condensed version of a homotopy type, which I will refer to as condensed shape, is closely related to the pro-étale topology and the work of Barwick, Glasman and Haine in the “Exodromy” paper.