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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!

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You are going to give one talk for 80 minutes? –  Mariano Suárez-Alvarez May 27 '12 at 1:34
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I'm pretty amazed anyone would schedule an 80 minute talk... that's well beyond the normal attention span of humans! Two 40 minute talks would be much better! –  rschwieb May 27 '12 at 1:53
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Well... if you know how to present content which is well-organized, one way to proceed would be: organize the content of the papers you want/have to talk about, and thereby put yourself in a situation you know how to handle! I am only half-joking here :) –  Mariano Suárez-Alvarez May 27 '12 at 1:55
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@HuiYu, your faith in experts exceeds mine! :D –  Mariano Suárez-Alvarez May 27 '12 at 1:58
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As Mariano suggests, definitely focus on organizing your ideas. The worst you could do is just list results (not that I think you would, I'm just pointing out the worst possible anybody could do). The more unifying ideas and interconnections you find, the more you will keep their attention. If they are already experts and you are presenting them as a reading, they are probably looking for how you analyze the contents. –  rschwieb May 27 '12 at 2:01
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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.

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@HuiYu Someone once told me that almost every talk needs one proof. This of course heavily depends on the subject matter. Maybe no proofs would be appropriate. Maybe there are three extremely interesting or novel proofs that should really make it into the talk. Spend some time thinking about which, if any, to include. BUT definitely do not overdo time in proofs :). –  rschwieb May 27 '12 at 2:07
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I am not doing an oral exam. But your advice is indeed very helpful! Thanks! –  Hui Yu May 27 '12 at 2:36
    
@HuiYu Okay. It just sounded like my oral exam presentation, that's all. Glad it helped! –  Neal May 27 '12 at 17:17
    
@rschwieb Fair. I have edited my answer to be a little less "anti-proof." –  Neal May 27 '12 at 17:19
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