How to approach a professor giving a presentation to work with him? I am a master's student in Applied Math with two undergraduate degrees in physics and math. There is a professor who is coming to my university to give a talk on his research, and I read his abstract for the presentation as well as part of his most recent publication and I really would like to work with him doing this over the summer. He is from a National Lab I have interned in before as an undergrad. There is almost no programs for graduate students at that lab and, since I am an international student, I am ineligible for the only one I found there. Is there any way for me to approach him to ask him for the possibility of working with him?

I have a pretty strong research background, and professors I work with at my university will be at the talk he is giving. I don't know if this could help me in any way.
I would send an email a week or so before the visit, saying about what you have said here and asking if the two of you could have a conversation during the visit. That would be better, I think, that surprising him at the talk. It will give him a chance to review any opportunities that there might be. He might also think of others who might be able to help you. 

If you just surprise him with a request he won't have that opportunity to think about it, and the circumstances of the visit might make it impossible to make contact in an ad hoc manner. 

But if there is nothing he can do for you directly, perhaps the contact can develop into something longer term.