4 problems

Let $\Gamma_g^r$ be the mapping class group of a genus-$g$ surface with $r>0$ boundary components. A right-handed Dehn twist is a Dehn twist with the positive orientation conventio…

Finiteness conjecture. The set $\mathcal{C}_{(M,\xi)}$ is finite.

Let a cusp singularity be a surface singularity whose link carries the contact structure associated with its cusp resolution, and let a rational dual mean that the dual cusp singul…

Non-Stein-fillability conjecture. The contact structures $\eta_{i,j}^n$ are not Stein fillable if $i>0$.