Peter Scholze (MPI Bonn)
Zoom stream of talk taking place at HU Berlin
One of the central notions of mathematics is the notion of a topological space: it captures the idea of a space with a notion of "nearness" of points. Originally motivated by the description of familiar objects like the real numbers or manifolds, it has since been used in virtually all areas of mathematics. However, sometimes, even within the field of topology itself, one finds the notion of topological space to be lacking some good properties. For example, it cannot meaningfully describe the idea of spaces with points that are "infinitely near, but distinct".
In joint work with Dustin Clausen, Scholze introduced a potential replacement for topological spaces, calledcondensed sets, which resolves many of these foundational issues. In this talk, Scholze will try to explain what condensed sets are, and how they improve on topological space
