There has been a great deal of recent progress in understanding different curve-counting theories in dimensions 2 and 3. On surfaces, the elusive BPS invariants of Gopakumar-Vafa have now been rigorously defined by many different approaches, which have also been shown to be equivalent. In three dimensions, the MNOP conjecture has been proved for many Calabi-Yau 3-folds, relating Gromov-Witten theory to stable pairs. Motivic and refined versions of DT theory have given new approaches to BPS numbers. For local surfaces there have been many calculations leading to rather complete results. This workshop will bring together the experts in the field to survey this progress and work on the many outstanding issues.