6 problems

Gromov's rational inessentiality conjecture. Then $M$ is not rationally essential.

Refined macroscopic dimension conjecture. The inequality

Gromov's conjecture. The macroscopic dimension of $M$ satisfies

Let $u$ be the solution of the parabolic Anderson equation with multiplicative noise, started from bounded initial data $u_0$. For $\beta$ as in the definition of the macroscopic H…

Let $M$ be a closed oriented $n$-dimensional manifold, let $\pi=\pi_1(M)$, and let $B\pi$ be a classifying space. If $f\colon M\to B\pi$ classifies the universal bundle, call $M$ r…

Strong Gromov conjecture. The classifying map can be deformed into the $(n-2)$-skeleton $B\pi^{(n-2)}$.