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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?

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    Maybe part of the problem is calling it a "colloquium", which generally implies that the intended audience is faculty and advanced grad students. You say you want the intended audience to be someone with an undergrad degree; your quoted passage sounds more like it describes third- or fourth-year undergraduates. So maybe you should begin pitching it as an undergraduate colloquium. Of course, it's possible you will find fewer speakers willing to try to describe their work to an (effectively) undergraduate audience. – Nate Eldredge Feb 20 '15 at 20:30
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    But what I'm saying is, the knowledge that you want your speakers to assume is the knowledge that a good third-year undergraduate in mathematics (not yet graduated) would have, or less. – Nate Eldredge Feb 20 '15 at 20:48
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    @NateEldredge that is not "generally implied." It is common that a colloquium means the audience is "the whole department," at least in theory, not just advanced grads and faculty. Typically this means a few very advanced undergrads, most of the grad students, and most of the faculty. Of course, due to the problem I describe colloquia often "turn into" only being for faculty and advanced grad students. Perhaps what you mean by generally implies is "in practice". Of course in pure mathematics the letter would have stronger math prerequisites, but this is not a math department. – WetlabStudent Feb 20 '15 at 23:10
  • I don't even understand the title for some of the colloquium talks in our physics department, which covers theoretical astrophysics, particle physics, biophysics, atmospheric physics, and climate science. – gerrit Feb 21 '15 at 16:08
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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.

  • Dangerous ideas is superb! I will try to steal it, let's see if it condenses. So, the format is, a speaker presents a talk answering the five questions, and then there is a free discussion? – Davidmh Feb 20 '15 at 22:17
  • @Davidmh Please do! As for the format: it was pretty free-form. We gave that as a starting point, encouraged people to view that as inspiration rather than requirements, and speakers took it in a lot of different directions. Some talks had a lot of discussion - others not so much. We also encouraged the audience to ask questions during the talk, rather than waiting to the end. – jakebeal Feb 20 '15 at 22:28
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I think there are a couple of layers to the problem:

  • The wording of your request to the speaker could be more clear. You should be very specific that you encourage graduate students to attend the department talks, so please keep the talk accessible for non-experts.

  • Some of the speakers may not be prepared or able to give a (I presume 30 to 50 minute long) "popular science" style talk on their current research. Some things are much more difficult to distil than others. Either that, or (donning my Hat of Cynicism) they're ignoring your request because they don't want to write a whole new presentation or they didn't read the email properly.

Perhaps you could ask the guest directly if they are able to distil their research down to a talk that is appropriate for a grad student not familiar with the field. If they decline, make it clear in the talk invitation that it is a specialized presentation. If the speaker agrees to do this, you should explicitly tell your grad students that the talk should be accessible for them. This will avoid them feeling as if they wasted their time attending high-level talks, thus they'll be more likely to attend the others.

  • My question may have been originally unclear. Can you edit your answer so it matches the fact that the target audience is not undergrads. – WetlabStudent Feb 20 '15 at 21:17
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I would suggest saying in the invitation "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. The target audience is first year grad students (and up) and academics in many different quantitative fields". I don't know what it means for a talk to be entirely self-contained, and that kind of wording encourages the inference that this is supposed to be a general public lecture -- then the remainder of the guideline shows how that's not so. Therefore I would expand on what the first sentence means.

I take it the problem is not that the talks are at too low a level, but rather they are at too high a level. Saying that "the audience is mathematically mature" may encourage reaching too high -- I tend to think of ABD grads and faculty as being "mature" in a discipline. If the problem is that speakers are interjecting arcana from physics or biology or unrelated areas of math, then you need to strengthen the "do not assume" clause. Make it a sentence on its own, and elaborate.

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    In this case, Wiki's characterization of "mathematical maturity" is very naive. (I'm not only being cute...) It's more about things like the pre-rigorous/rigorous/post-rigorous phases popularized by Terry Tao, for example. – paul garrett Feb 20 '15 at 23:14
  • @paulgarrett I really love Terry Tao's phrases "pre-rigorous/rigorous/post-rigorous", however, wikipedia's definition, of mathematical maturity paraphrased as comfortable with abstraction is how it is most commonly used. For example, see this matheducators.stackaexchange question matheducators.stackexchange.com/questions/1403/… – WetlabStudent Feb 21 '15 at 15:18
  • @WetLabStudent, I agree, that's how the phrase is often used, but my point is that it misses the mark, especially RE peoples' self-assessments. And, anyway, declaring that the prereqs are this-or-that doesn't magically make it so, either. – paul garrett Feb 21 '15 at 15:37
  • @paulgarrett yes, I think we agree on that. – WetlabStudent Feb 21 '15 at 19:20

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