Should I ask to work on professor's project? I have a professor that I've gotten to know pretty well. Currently we're going through and learning about a newer area of mathematics just for the fun of it. It was my idea to do it and now he's looking to do more with it. He wants to do research on an application of this area of math next summer through next fall. We plan to continue studying this area for this coming apring semester as well, but I would love to actually work on this project with him.

Because we know each other so well, I think he would enjoy me working with him on it overall. The problem is that he's going abroad to do the research. What I want to know is if there's any potential for me to work with him on this and on whether or not I should ask him for the opportunity? Or should I just wait and see if he approaches me on it?

I should point out that I will have graduated by next summer.
Yes, you should ask! Don't be shy -- there's nothing at all to lose. In the worst case, he'll point out that the logistics of collaborating remotely are hard, or something like that. No one is ever upset that someone is enthusiastic about working with them. If you're worried about the lost opportunities of doing research with someone more local: having a project you like and an advisor you work well with seems far more important than local convenience here -- it's not like you're in a field that needs a lab and hands-on training.