4 problems

Counting conjecture. There exists a constant $C(M)$ such that

Let $G=(V,E)$ be a non-acyclic graph, with a fixed-point-free involution $\mu:V\to V$ and, for every vertex $v$, a bijection $\sigma_v:\delta(v)\to\delta(\mu(v))$. Assume that…

Let $F_n$ be a free group, and let a list of cyclically reduced words in $F_n$ be minimal and diskbusting, meaning that it cannot be decomposed into a proper sublist with the same…

Let ${\cal M}$ be a closed hyperbolic $3$-manifold. A surface subgroup is the image of the fundamental group of a closed surface of genus at least $2$ under a map inducing an injec…