I would prefer for my girlfriend to not hang out with her ex.
What is your reason for not wanting her to hang out with her ex anyway?
I don't like him. He cheated on her and made her feel miserable.
It's okay to not want your girlfriend to hang out with her ex if he treated her badly. However, who she sees on her own time is ultimately her own decision, and you shouldn't try to control it.
I'll need to show my sexual interest in her more.
This may be a good idea! Just know that trust is very important in a relationship and if you feel you cannot trust your partner then you should talk to them about it. Without trust it is going to be difficult to be happy in your relationship.