13 problems

Let $X$ and $Y$ be compact piecewise Riemannian spaces, and define … Assume that $Y$ is simply connected. Gromov's growth conjecture. The function $g_{[X,Y]}$ is always asymptotic…

Let $X$ and $Y$ be finite complexes, with $Y$ simply connected. For $L>0$, consider the mapping classes in $[X,Y]$ having representatives with Lipschitz constant at most $L$. Gromo…

Let $G$ be a group of exponential growth, let $A\leq\operatorname{Aut}(G)$ be a finite subgroup with $|A|=n$, and let $X=(G,A)$ be the corresponding coset group. An $n$-valued dyna…

Alahmadi–Alsulami–Jain–Zelmanov conjecture. The following are equivalent:

For the infinite series of types $A_l$, $B_l$, and $D_l$, let $G_P^{\mathrm{dual}+}$ be the corresponding dual Artin monoid and let $N_{G_P^{\mathrm{dual}+}}(t)$ be its skew-growth…

Let $P$ be a finite-type Coxeter graph with rank $l=\operatorname{rank}(P)$, let $G_P^{\mathrm{dual}+}$ be its dual Artin monoid, and let $N_{G_P^{\mathrm{dual}+}}(t)$ be its skew-…

Conjecture 1. The polynomial $\widehat{N}_{G_P^{\mathrm{dual}+}}(t)$ is irreducible over $\mathbb Z$, up to the trivial factor $1-2t$ for types $A_l$ with even $l$ and type $D_4$.

Let … be the cancellative monoid in Example 3, and let $G$ be its corresponding group. Its spherical growth function is $1/(1-t)^4$. Virtual $\mathbb{Z}^4$ conjecture. The group…

Let … be the cancellative monoid in Example 2, and let $G$ be its corresponding group. Its spherical growth function is $1/(1-t)^3$. Virtual $\mathbb{Z}^3$ conjecture. The group…

Let $G^+_{\mathrm{B_{ii}}}$ be the monoid whose spherical growth function is … and let $G_{\mathrm{B_{ii}}}$ be its corresponding group. Virtual $\mathbb{Z}^4$ conjecture. The grou…

Let $\langle L\mid R\rangle_{mo}$ be one of the three monoids considered in the appendix, and let $\langle L\mid R\rangle$ be its corresponding group. Virtual abelianity conjecture…

Let $\Gamma_M$ be an Artin monoid of affine type, and let $h_{\Gamma_M,G}$ denote the period associated with its growth function, equivalently the number governing the poles on the…

Let $(\Gamma,G)$ be a cancellative infinite monoid, with growth function … and growth partition function … Write $r_{\Gamma,G}$ for the radius of convergence of $P_{\Gamma,G}(t)$.…