Colloquium Guidelines
A colloquium talk should be in 3 roughly equal-length parts:
(1) An introduction understandable by begining 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 subarea, 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.
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