How to motivate speakers to give less specialized talks at a "colloquium?" Our applied math department is beginning to have a serious attendance problem at our colloquium. The appropriate level for our colloquium is that any person with an undergraduate degree in a quantitative/theoretical field should be able to follow the talk as long as they are paying close attention. 

In an invitation letter to our speakers, who are mostly faculty members at other Universities in a variety of fields but also include some faculty at our university, we say 


  "Your talk should be entirely self contained. You can assume the audience is mathematically mature and has a solid understanding of undergraduate real analysis and linear algebra but do not assume any prior knowledge in physics, biology or more specialized mathematics. Of course feel free to talk about such topics, just be sure to explain all basic concepts needed to follow the rest of the presentation as soon as they come up." 


Despite this warning, speakers go on, as usual, giving seminar level talks. Graduate students and the few advanced undergraduates that used to attend have basically stopped attending, which looks bad on our department, and lowers graduate student morale. Note the target audience is not undergrads. The target audience is first year grad students (and up) and faculty from many different quantitative fields.

I think part of the problem is that speakers assume applied math means "The math done in my field of research". They don't understand despite us linking to our graduate student's list of research interests in the email that applied math is extremely broad. Some researchers will have never taken probability theory or optimization and some who work in theoretical computer science haven't studied a differential equation since their sophomore years of college. And science backgrounds outside of math will be even broader.

Besides adding the request in our email, that the talk not be too technical, is there anyway to prevent speakers from giving talks that are too specialized or advanced?
One important thing to do is to be more choosey about inviting speakers who you know are capable of presenting to a broad audience.  Some people will never give an accessible talk, no matter what you do.  Others are good at speaking to a broad audience.  Some good ways to find such speakers:


People who do cross-disciplinary work are often really good at this, since they are generally used to speaking to non-specialists (i.e., people who are specialists in the other disciplines that they work with). 
Look for people who have recent survey publications which are broadly accessible, or who have had recent articles or other publications in the popular media.
If you go to conferences and workshops, look for people who give accessible talks, even to a specialist audience.  The best speakers will always frame their work accessibly, even when the meat of it is extremely specialized.


Once you have invited a speaker, make the speaker give you a full abstract, as well as a title.  If the abstract is getting too technical, it's a bad sign for the talk.  Send it back with request for revision to attract a broader audience.  This can help people adjust expectations, though you can never prevent a speaker from speaking badly once they've begun.

If you feel brave, you might even explicitly challenge your speakers more in the information that you send them.  My favorite series that I have ever been involved in organizing was the "Seminar on Dangerous Ideas" that I helped create when I was a graduate student, and which ran for about five years.  This seminar was really trying to push people outside the box, and one of the ways we did it was to ask the speakers to address "the five questions",  which included things like "Why should I fear your research?" and "What should I tell my mom about it?"  Many of the best talks that I have ever heard were in this series, because the challenges that we gave were able to create an atmosphere in which academics felt safe to say things they otherwise would not.

You'll also need to work to revive your existing seminar series.  A good way to do that is to line up several speakers in a row who you are certain will have broad appeal and be able to give a good talk.