7 problems

The generalised Casson conjecture. For every $\alpha\in\mathcal{A}(\mathcal{T},\mathbf{s})$,

Let $M$ be a compact orientable 3-manifold with empty or toroidal boundary. Define … where $r$ runs over all odd integers, and let $\operatorname{Vol}(M)$ be the simplicial volume,…

Let $P(u)$ be a flexible polyhedron in the sphere $\mathbb{S}^n$, where $n\ge 3$. Replacing a vertex by its antipode means replacing that vertex of $P(u)$ with its antipodal point…

Let $N$ be a $3$-manifold with non-empty boundary and let $\mathcal T$ be an ideal triangulation with edge set $E$. Let $\{\mathbf b^{(r)}\}$ be a sequence of colorings of…

Let $M$ be a closed oriented $3$-manifold and let $L$ be a framed hyperbolic link in $M$ with $|L|$ components. Let \\{\mathbf a^{(r)}\} be a sequence of colorings of the compon…

Let $\Gamma$ be a planar $3$-connected graph, let $\overline{\Gamma}$ denote the associated maximal-volume proper generalized hyperbolic polyhedron, and let $col$ be any $r$-admiss…

Let ${\mathcal{T}}_\ell$ denote the space of truncated hyperbolic tetrahedra whose edge lengths satisfy the constraint defining ${\mathcal{T}}_\ell$, and let $\Delta_\ell$ be the r…