Dianthe Basak (Jussieu) : What's True and What's Right: the Ext group, Condensed Mathematics, and the Solovay Model

The so-called Cauchy functional equation

f(x+y) = f(x) + f(y)

for a function f : R -> R, marks one of the simplest instances of mathematical intuition bumping up against the wildness of mathematical truth. It is the first of a family of equations which define the so-called Ext groups of the circle group R/Z. In any standard universe of set theory, these equations have wild, ill-behaved solutions. This leads us to ask: what are the "right" solutions, and similarly what are the "right" Ext groups of the circle, and where do the right solutions come from? Two broad directions towards answering this "extra-mathematical" question have emerged: that of Clausen--Scholze's condensed mathematics, and that of Solovay's universe of "ideal" mathematics. Surprisingly, they converge upon the same idea, which will be the subject of the talk. The talk will be aimed at a broad audience; the few technical results mentioned are recent joint work with Nathaniel Bannister.