Sebastian Wolf (Copenhagen): Higher Compacta and fundamental groups in rigid geometry

The category of condensed anima, introduced by Clausen and Scholze, is a setting for homotopical objects that carry an additional “topological” structure. We will begin by studying the subcategory of coherent condensed anima that forms a higher analogue of compact Hausdorff spaces. It turns out that many of the formal properties of (sheaves on) compact Hausdorff spaces carry over to this more general setting. Using some of these tools, we will then turn to examples arising from rigid geometry and use this perspective to study fundamental groups of rigid spaces.