How do you deal with a girl who consistantly talks about her ex? It's not my relationship! Why talk to me?

First, the only way to know is to talk to her find out why she wants to talk about him to you.

I’m apparently different in this. I want to know about a person’s past experiences and relationships. It will tell me a lot about the person and how they handle themselves in a relationship. I will ask what they have learned from those relationships so I can see how they have grown as a person. Or are they just reliving the same things over and over again and not learning from them. Will they give up at the first bump
In the road or do they face the bump and include me in on what to do about it?

Take advantage of what she is telling you to learn more about her. What did she like about the relationship and what did she not like about it. What did she learn. What are her expectations now that it is over and the two of you are seeing each other. Etc. some people sort through things by talking. Some do it by journaling. And since she is talking get her to tell you what you want to know. If you shut her down she will think she can’t talk to you about anything and I don’t think that would be good. But I’m all about full disclosure so I can learn about who you are.

If that isn’t what you want then tell her. Better to get it out on the table now to determine if the two of you are compatible. And when I say talk to her I am not talking about giving her judgemental statements. I’m talking about asking her questions to make her think and decide for herself how she should feel so she can move away from it and see you for who you are. And for you to know if you are the right person for her or she for you. She wants to know you aren’t that guy and you won’t be that guy and that being with you is a good choice.

How you respond to this will tell her a lot about you.