2 problems

Let $M$ be a closed Riemannian manifold whose fundamental group satisfies $(T_n)_{L^1}$, and suppose that $M$ is $(n-1)$-connected. The $(T_n)_{L^1}$ waist conjecture. Does the fam…

Let $G$ be a simple Lie group of higher rank $d\ge2$ with finite center, and let $X=G/K$ be its associated symmetric space. The higher-rank waist conjecture. The family of finite-v…