Probability, and thus multivariate calculus and partial differential equations. Linear algebra. Convex Optimization, and thus multivariate and partial differential equations. Some principals of statistics is usually helpful
Why do you need partial differential equations? I don't think you necessarily need any knowledge of differential equations to do ML, though the top ML people certainly would know it because of their general math education.
I spent a lot of time messing with PDEs as a student but sadly that knowledge hasn't been very useful - I've only seen them come up in quite specialised areas like optical flow...