6 problems

Let $G$ be a group such that the classifying space for proper $G$-actions, $\underline{E}G$, has a finite model. Let $A_{\operatorname{ho}}(G)=\pi_G^0(\underline{E}G)$, let…

Let $G$ be a group and let $F$ be a field of characteristic zero. Define … where the colimit uses induction along inclusions of finite subgroups. Covariant representation-ring conj…

Antolín, Martino and Ventura's meta-conjecture. For any “reasonable” sequence $M=(\mu_n)_{n=1}^\infty$ of probability measures on $G$, we have $\operatorname{dc}_M(G)>0$ if and onl…

Protasov–Slobodianiuk conjecture. Every infinite group $G$ of cardinality $\varkappa$ has a partition as above such that

Strong orbit-equivalence rigidity conjecture. If $G$ and $H$ are strongly orbit-equivalent, then

Orbit-equivalent groups conjecture. $G$ and $H$ belong to the list above. This would strengthen the main theorem by removing its assumption that the groups are not 2-transitive. Th…