This is the fifth talk in the Minerva Mini-course, Applications of o-minimality in Diophantine Geometry, by Jacob Tsimerman, University of Toronto and Princeton's Fall 2021 Minerva Distinguished Visitor.
We discuss conjectures and results in unlikely intersections using o-minimality. We study the Zilber-Pink conjecture and explain how number theoretic inputs like the Masser-Wustholz isogeny bounds and height bounds factor into the current methods.