How to present a paper? I am going to present several papers to an audience. I have read through all the papers and have a clear idea about them.
But this is the first time I have ever presented papers, and I am guessing that many of you have done this many times. So I am sure I can get a lot of good advice from you on how to do this.
I have about 80min to talk about 2-3 papers. They are about operator algebras and my audience are experts who have been working in this field for at least 20 years.
Any advice would help!
Thanks!
 A: This sounds like a presentation for an oral examination.  I'm going to give you some tips I found helpful in preparing my oral exam presentation, which was over one paper and several supporting papers.  (I am assuming that your goal is to present papers, not proofs.  I don't mean to say, don't include proofs when you're presenting several papers, but that if you focus on the details of any proofs, you run the risk of losing your audience's interest in a thicket of technicalities.  rschwieb has a very good comment below.)
Rehearse the talk beforehand.  Make sure that you don't run over time.
You have probably spent weeks reading these papers.  You need to distill those weeks down into 80 minutes of clearly explained ideas.  If I were giving the presentation, I would give the big-picture logical structure of the papers.  I wouldn't present any details unless you are asked.
I'd try as best I could to make that big picture logical structure a story.  Mathematicians are just human, after all, and we follow stories better than logic.  What motivates these papers?  What common themes tie them together?  The motivation is the problem you have to solve, the themes are the characters, the plot is how the themes come together to solve the problem.
I think that finding common themes and turning them into a story is the most important part of this exercise.  By doing this, you'll get to show off how discerningly you know the math (since you have to know it well in order to distill it down to common themes and then focus on those).  You'll also have the pleasure of stepping back and looking at the big picture as you prepare, instead of losing yourself in yucky details.  Finally, you'll also be able to tell a (hopefully semi-exciting) story instead of just reciting "theorem ... proof ... lemma ... proof ... theorem ... proof ..." while your audience dozes off.
One other tip.  Before starting, I'd outline the talk narrative and every five or ten minutes, as the flow of the material allows, remind the audience where we are in the narrative.  This helps put the story in perspective, is a temporary check for anybody tuning out, and (frankly) reminds the audience that the talk isn't going to last forever.  It also helps hammer the chief ideas home.  In any speech, you do three things: tell them what you're going to tell them, tell them, and then tell them what you told them.
