Condensed abelian groups and solid completion

I will describe a modification of the notion of topological abelian group, called "condensed abelian group".  This modification has favorable categorical properties, and in particular it is possible to define a very well-behaved completion functor, the "solid completion", which is suitable for non-archimedean geometry in the style of Tate and Huber.  This is joint work with Peter Scholze.