What are the key features of a short (15 min) conference presentation?
How can I balance the details of research without losing the audience on key points?


From my perspective, the key to giving a 15 minute talk is to omit all of the details.  Many audience members don't care, the few who do can read your paper, and in any case it's impossible to convey any serious details clearly and correctly in such a short time.  If you try, then much of the audience will stop paying attention; you'll end up wasting their time and missing a great opportunity to present your work.  Instead, your goal should be to ensure that everyone leaves with some understanding of what you've done, and that some of them are inspired to learn more.

This means you should focus on the big picture.  What did you do, how and why did you do it, and what have we learned from it?  In mathematics, I'd focus on context, motivation, definitions, theorem statements, examples, and intuition.  It's OK to give a brief proof outline or sketch, but nothing detailed or complicated.  If you can't summarize it in a few sentences, it's too complicated.

There are various ways short talks can go wrong.  For example, some of them try to compress 30 minutes of content into 15 minutes by talking fast and barely explaining anything, while others simply omit the background and context needed to understand the presentation.  However, there's a common difficulty behind many bad talks: they focus on the speaker's desires and goals rather than the audience's.  Ultimately, you need to design your presentation to fit the background and interests of the audience and the time available, rather than what you wish you could tell them.