Mathematics Problem Archive

Let $\Gamma$ be finitely generated and let $\{H_n:n\geq1\}$ be a property-$\tau$ family of finite-index normal subgroups. Does the chain $\Gamma_n=\bi...

Let $\Gamma$ be finitely presented with a chain of finite-index normal subgroups having trivial intersection and property $\tau$. Must $\Gamma$ contai...

For a free action of $\Gamma$ on $X$, is $\operatorname{cost}(\Gamma,X)=\operatorname{cost}(\Gamma,X\times X)$ for the diagonal action on $X\times X$?...

Given a graphing of an equivalence relation, is there a subgraphing whose cost is arbitrarily close to the cost of the relation?...

Can a nonabelian free group $F$ have a nontrivial pseudocharacter invariant under $\operatorname{Aut}(F)$?...

Let $M$ be the set of measurable real functions, and define $H_f(x,y)=(x,y+f(x))$ and $V_f(x,y)=(x+f(y),y)$. What group is generated by $\{H_f:f\in M\...

In Gromov's density model with generators $a,a^{-1},b,b^{-1}$, choose $3^{nd}$ relators independently and uniformly from the reduced words of length $...

Let $\beta$ be a nondegenerate bilinear form on a finite-dimensional real vector space $V$, and let $G=\operatorname{Isom}(\beta)\subset GL(V)$. Which...

Do closed hyperbolic $3$-manifold groups have finite-index subgroups that embed in a word-hyperbolic reflection group?...

Does every freely indecomposable cubulated hyperbolic group contain the fundamental group of a closed hyperbolic surface?...

If $M$ is a closed $3$-manifold, when does $\pi_1M$ act on the affine building for $SL(4,\mathbb{R})$ so that the quotient retracts to $M$?...

Which subsets of $S^2$ can occur as limit sets of convex-cocompact Kleinian groups?...

Characterize the limit sets of graph Kleinian groups and iterated graph-Kleinian groups. A graph Kleinian group is a convex-cocompact Kleinian group f...

Can there be a degenerate Kleinian group that is not the fiber of a fibration and has algebraic trace field?...

Is there a singly degenerate Kleinian group for which all matrix entries of all group elements lie in one fixed number field?...