Some cases of the Zilber-Pink conjecture for curves in $\mathcal{A}_g$

The Zilber-Pink conjecture is a far reaching and widely open conjecture in the field of unlikely intersections generalizing many previous results in the area such as the Andre-Oort conjecture. We discuss this conjecture and how some cases of it can be established for curves in $\mathcal{A}_g$, the moduli space of principally polarized g-dimensional abelian varieties, following the Pila-Zannier strategy and bounds for the values of the Weil height at certain exceptional points of the curve.