First, some factual information: the talk is for 60 minutes, including at least 5 or 10 minutes for questions. NEVER go overtime :) Usually I'll need the abstract and title of the talk around noon on Thursday the week before (for the seminar announcements).
Besides writing a nice and understandable abstract, the best way of getting lots of people come to your talk is inviting them :)
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Now, let's get to the main point: I thought I'd try to write some suggestions about preparing the talks and abstracts. In fact, there is mainly one advice :)
I think it's almost impossible to underestimate the correct level for your talk, so if at doubt (and even if not), it always helps to make it more elementary and spend more time talking about the background and motivation for the area. It is quite hard to realize that the concepts that seem so natural and easy to you, in fact are not! Just remember how much time you've already spent thinking about them.
Of course, there are no clearly defined prerequisites for the Student Colloquium. Ideally, the talk should be understandable even by first year graduate students. While this may not be always possible, you certainly shouldn't assume more than qual-level knowledge.
On the other hand, people like to hear some fancy words and feel that they've learned something cool. So it certainly IS a good idea to try to spend maybe the last 10 minutes talking about advanced stuff, your work, or some important conjectures.
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All the same is true for the abstract. In fact, even more so, because it's mostly the abstract that determines whether you'll get a broad audience or just a couple of other students from your area. So write generally about the field, background, and motivation! Also, it can be a good idea to ask someone way outside your area of specialty to read the abstract. If they can't understand it, it's too difficult. I can also try to provide such feedback (so far over half of the abstracts I got were way too hard) :)
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But I certainly don't want this all to sound demotivating! Of course, it is much easier to give a rather specialized talk about the stuff you're doing. But at least for me, preparing and giving an elementary talk is a great excuse and impulse to think about my area much more broadly, ultimately providing motivation even for myself! And I guess that in mathematician's life, being able to convince others how important and interesting is your area, is an extremely valuable skill - so why not start practicing it with this talk?
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However, if you want to give a technical talk about the intricacies of your proof, then the Student Colloquium is almost certainly not the right place for you :) Maybe it would be a nice idea to have a follow-up seminar, where people could continue with a more specialized part of their talks for a smaller audience.
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[But of course, don't take anything on this page too seriously. I'll greatly welcome any suggestions, comments or discussion :) ]
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