How to give a short talk at big math conference (section talk)?

Question

Context:

Very big math conferences are often structured in the following way: there are key note speakers, but also sections on more specific topics, as well as satellite workshops on quite narrow subjects. This question is about the second type of talk. Due to the size of such conferences, the talks maybe rather short (20min, 30min).

Such sections (Algebra, Topology, Geometry, Probability theory, etc.) are still very broad. The organizers might make an effort to group similar talks together within different daily sessions, but it should be taken into account that many conference participants will follow all daily sessions of one section.

Question:

How to approach such a short talk?

How to find a good balance between bringing the own results across to the broader audience without having to spend all of the talk explaining background, and saying something interesting to experts?

It seems find that in a typical 1h seminar talk it is easier to provide something for everybody: listeners who have not seen the basic constructions of the topic, and experts of the field.

Answer 1

The advice is the same as for any talk, only moreso: Think of your talk as an advertisement -- your goal is to get people interested enough so they will look up and read your paper (or, in this case, invite you to their seminar to talk about it in more detail). Specifically:

• Assume no one in the audience is an expert on your topic. (Seriously. It's hard to underestimate how much everybody else knows about something you spent years studying.)

• The most important question to address is why should the audience care about your work? This question needs to be answered by slide 2 at the latest, and it doesn't hurt to remind them on the last slide as well. This is easy if you solve a long-standing open problem, but anything in the direction "if you have such-and-such a problem, my result will help you" will do. (If you really cannot come up with something, at least tell them why you care about the work -- presumably, some aspect of it was fascinating enough to make you finish it.)

• Skip the details. Honestly, if in doubt, leave it out. Focus on a few core ideas, and try to get them across as plainly as possible. If your main result needs two slides of assumptions or notations before you can state it, see if you can find a more specific (non-trivial) setting where it will fit on one slide. Don't try to give a blow-by-blow proof, but stick with two or three high-level bullet points ("Proof uses Galerkin approximation, compensated compactness, and the embedding of X into Y").

(Also, since this is such an old question, you probably already went to the very big meeting. What did you hope to get out of hearing those talks? In hindsight, which ones did you take the most away from? Keep this in mind when preparing the next talk.)

Answer 2

Be sure to focus on YOUR work. Compress the background information to only that which DIRECTLY connects to your work.