Presenting a paper: Do's and Don'ts? I was wondering what would be the best way to present your paper at a conference, if your paper is selected for "short communication", lasting for about 15 minutes?
Should you concentrate on the main results or the proofs?
And what should a first-time presenter be wary of?
Thanks in advance.
 A: I'm sure that this is not the immediate advice that you need for this question, but I urge you to keep this in mind: go to many talks and make notes about what you like and what you dislike about them. Then try to objectively assess yourself on these points... In the long run, this habit can improve your talks quite noticeably.
A: Practicing your presentation helps.  With a recording device or a test audience, you
can get valuable feedback concerning the style and timing of your presentation, among
other things.
In addition to verbally presenting a paper, there is supplementing the presentation.
Sometimes the interested audience member will want more.  You might prepare ahead of time some business cards, or even slips of paper, to hand out.  They should contain your contact information, the title and time of your talk, and optionally a URL to a file that contains details of your presentation that you would like to have given.  This is one of the things I will do for my 15 minute presentation.  If you are really on top of things, you could have something ready to receive the member's contact information as well.
Gerhard "Ask Me About System Design" Paseman, 2010.06.28
A: Perhaps this is addressed in the previously linked articles, but you should avoid merely reading from your slides (if you are giving a slideshow). For one thing, if you can read the entire talk directly from the slides, then the slides probably have too much text on them. Second, you're a lot more likely to keep your audience engaged if you're not so obviously following a script.
I've heard that in some academic fields, people go to conferences to "read a paper," not to "present a paper." When I go to a presentation, I'd prefer not to be read at.
A: The first priority is to state your main results and explain why they are interesting (e.g. how they fit in with related work).  With only 15 minutes you do not have much time to discuss proofs, but it is nice to give a brief outline of the proof of your main result and what is involved.
As a first-time presenter, I would watch out for the following:
First, as someone commented, it is crucial to not go over time.  Don't try to cram too much in.
Second, watch out for the mechanical aspects of the presentation, e.g. is your print large enough to read, and is your voice loud enough to hear.
Third, strive to emphasize the most important points and not get lost in less important details.  This is especially important when you only have a short time to talk.
Fourth, know your audience, so that you have some idea what you can assume is known and what you need to review.
A: I can't do anything better than advice your reading the following:


*

*J.A. Gallian, Advice on giving a good powerpoint presentation, Math Horizons, April. 2006:25-27


(It is a list of dos and don'ts, short and sensible; of course the same holds for OpenOffice and LaTeX slides, and most advice - also for classical blackboard.)
Additionally, it helps to watch people who are good at giving lectures/talks. One great event is TED.com (surely worth watching). While there are no research mathematical lectures - art of performing a talk, conveying ideas, focusing people's attention and emphasizing the main points is generally crucial.
A: The following is not my invention, but I cannot recall where I saw it to give a proper credit. Anyway, I myself follow this advice for all of my own talks. Before preparing your presentation, ask yourself: 

If there were only one thing I can tell the audience, what would this thing be?

Now, when you have a clear answer, keep it in mind preparing the talk (and don't forget to state it in the most explicit form)!
A: I think the other answers cover the basics well - and as with all things in life, it is more important to do the basic things right than to be brilliant. Having said that, here is the most important question to ask yourself in order to give a really good talk:
How is what I am going to talk about connected to things the audience knows?

If you connect your content to things your audience knows, they may find short arguments persuasive rather than unconvincing or out-of-the-blue. They will understand better why your results are interesting. They will ask more engaging questions, and will more likely give you useful feedback and ideas. They can appreciate new insights better if they come in context.
The answer to this question is typically much longer than you might think. And often it's really impossible to know the full answer. (It's one of the natural advantages of senior mathematicians as speakers that they will be able to give themselves a more complete answer. A good hint at parts of the answers may lie in some of the questions you got the previous time you gave the same talk - maybe especially those questions that didn't seem to make sense.) Nevertheless, it's useful to think about the question.
A: Some general points I find important:


*

*focus on the main results

*don't spend time with proofs (people can read those them self)

*don't give any hand-outs (this just distracts people; wastes paper)

*put the important points on the slides, talk about what is not on the slides

*don't put too much into the slides, make the fonts big and readable

*humor is useful to keep people paying attention. this might be more difficult with a math paper than for example with a paper from computer science, but there are still posibilities to use humor.

*talk loud and clearly, don't turn around to look at the slides or text.

*use the blackboard to answer questions and to give examples (don't put the examples in the presentation)

A: Two further remarks. 
The time devoted to one aspect of your work has not to be correlated to the time you spent on it.
Do not speed up because you see someone nodding or sleeping.
A: Do: Use black board.
Don't: Use computer.
This is a good read: www.ams.org/notices/201302/rnoti-p235.pdf
