Jérémie Marquès (Università di Milano) will give a talk on
Ultraconvergence 1-spaces
Abstract:
There are many notions of space in mathematics: topological spaces, locales, schemes, toposes… In this talk I will present yet another one: ultraconvergence 1-spaces. I will explain where they come from through their relation to topological spaces, toposes and logic. Examples of ultraconvergence 1-spaces include the space of models of a geometric first-order theory, as well as the category of complete metric spaces.
This talk is based on joint work with Sam van Gool and Umberto Tarantino, building upon Makkai’s work on ultracategories.
Preprint: https://arxiv.org/abs/2508.09604