The situation in math is slightly different than other fields and so it is reflected in the hiring process.
As a general rule, it is always good if your potential employers (i.e. the professors in the related math department) will know you beforehand, and definitely if you have means to go and present your work in a seminar go do that.
If you happen to meet in a conference, go introduce yourself and shake hands with him.
Approaching a professor directly out of the blue (i.e. just emailing) might not be the best thing, you might get overlooked or something, it might irritate the professor, the usual best idea about emailing someone without prior meeting with him is to arrange a more senior person (i.e. your adviser) to email him and tell him about you and inquire about your status as a future hire. It is also OK to email him with your preprint before putting them up in the Arxiv (again, do everything in coordination with your adviser, as it would be best to write explicitly in the email - my adviser, Prof. MATH, asked me to send this article to you for your consideration) and then end up in p.s - I'm about to graduate, and I would like to consider me as a post doc.
You have mentioned some future work, after the initial contact, you may bring that up (again, it would be best to ask your current adviser about it, maybe there are better experts to contact, maybe things are easy, you don't want to discourage your future employer so it is a delicate situation). Definitely you should write that future direction on your research statement you upload to mathjobs.
Regarding ''securing'' - most post-doc positions in math are (junior) faculty, means that there is some teaching involved, and the hire need to be accepted by the department. There's no extensive voting process like the one done for senior faculty hires, but usually there is some post-doc committee sifting through the applications, short-listing and so on.
The professor you've mentioned can ask to consider you to the short list.
Moreover, in many cases the spots are allocated between the different ''groups'' namely in there are X places, Y will be analysis, Z will be NT, W will be dynamics, P will be algebra, Q will be applied and so on. So you should check that this professor you mentioned can grease the wheels inside his group in order to get you high up the ranks.
In the end, the best thing you have is your recommendations (and this is what carries the most significance to your hire). Make sure that they are good and when hiring season is in play (say December), make sure your adviser is taking care of you and encouraging his friends to hire you.