Colloquium Guidelines

A colloquium talk should be in three, roughly equal-length parts:

1. An introduction understandable by beginning graduate students in the department. State the motivation, and outline what you achieved. Not all epsilons and deltas needed here. No area-specific prior knowledge should be assumed.
2. A middle part that is accessible to every grad student and faculty member in your discipline. Undergraduate background in that discipline can be assumed.
3. A last part addressed to faculty members and advanced grad students in your sub-area, providing additional details, highlighting important issues, explicating the significance of the material.

(If you are in group 1 and are watching a talk, parts 2 and 3 are useful in getting some feeling for how deep the area is, and to see how others react to it. In any case, you didn't waste your time, since (1) was accessible.)

It is hard to get people to agree to structure a talk as above, but one may always suggest it when inviting speakers. My experience is that it works quite well.