Following up with professor after PhD rejection I met briefly with a professor last year and showed him a poster of my work which was not good at that time (It was some sort of a presentation in which we show our work and research). Then I decided to apply for a PhD so I emailed him and he told me to apply. I knew that he will be coming to the same presentation this year so I emailed him again saying that might be an opportunity to talk in person. He never returned my email. That was two months ago. Ten days ago I was rejected from that university (I guess he made the decision). Yesterday, I presented my work in front of the whole audience which was much better than the one I presented last year (Even though I was rejected, I tried to impress him). I didn't talk to him directly then. Just now he viewed my profile on linkedin (Which he did multiple times previously awhile back).      

Does it make sense to follow up now? At to least know why I was rejected and why the sudden interest just after my presentation? I know it is very difficult, but would it even be possible to flip the rejection into admission now if he decided to?
I know being rejected is extremely disappointing but be careful to not read too much into the situation. It is quite possible that this person does not remember that you applied to the program, did not review your application at all (even though you requested them as a supervisor), or wanted to admit you but could not because of funding limitations or departmental politics.

Keep in mind that the fact that you know that this one person has viewed your LinkedIn profile is, honestly, a little creepy. The fact that you are reading so much into the "sudden interest" that comes from visiting the website of a person you see presenting seems to be a little obsessive. It is totally normal to search for more information about people one sees presenting work.

If you are honestly interested in knowing how you can improve your graduate applications in future years, and if you think that you might learn things that you will actually be able to improve your application, emailing might be helpful. That said, if s/he doesn't get back to you, keep in mind that it might just be because s/he is busy or flaky and responding to the students one has not admitted is often a relatively low priority item on a very long list of more urgent things.