# Mathematics Colloquia and Seminars

(This lecture is part of BATS) Let $\Gamma \subset \text{Isom}^+ (\mathbb{H}^3)$ be a quasifuchsian group freely generated by two elements with parabolic commutator. The manifold $\mathbb{H}^3/\Gamma$ has a convex core $C$ whose boundary, a union of two punctured tori, comes with two pleating laminations. These laminations define an infinite (topological) ideal triangulation $T$ of the interior of $C$, which is canonical in a combinatorial sense. We turn $T$ into a true'' geometric triangulation via Rivin's maximum volume principle, and show that $T$ is also canonical in a different, purely geometric sense, a result first conjectured by Akiyoshi, Sakuma, Wada and Yamashita.