4 problems

Goldschmidt–Sims conjecture. When both $m$ and $n$ are prime, there are only finitely many faithful $(m,n)$-amalgams of finite groups.

Sticky matroid conjecture. No matroids other than flat-modular matroids are sticky; equivalently, if a matroid has a non-modular pair of flats, then it is not sticky. The conjectur…

Let $M$ be a matroid. An extension of $M$ is a matroid $N$ on a ground set containing the ground set of $M$ such that $M=N|E$. An amalgam of two extensions $N_1,N_2$ of $M$ is a ma…

Tits's uniqueness conjecture. Groups of Kac–Moody type are uniquely determined by the fact that they act on some twin-building, together with Moufang foundations.