We survey the complexity class $\exists\mathbb {R} $, which captures the complexity of
deciding the existential theory of the reals. The class $\exists\mathbb {R} $ has roots in two …

A combinatorial neural code $\mathscr C\subseteq 2^{[n]} $ is convex if it arises as the
intersection pattern of convex open subsets of $\mathbb R^ d $. We relate the emerging …

Every ordered collection of sets in Euclidean space can be associated to a combinatorial
code, which records the regions cut out by the sets in space. Given two ordered collections …