I just got interview to teach college (of applied science) compsci student math. This is the first time I get this type of interview. The type of interview is called a "hearing" where a dozen people (called the "comittee") are to sit in front of me and I am to introduce myself then give a short lecture of about 20minutes (seems to be unrealistic imo) about a math subject in which I have expertise in and that is a topic related to my current research. Another restriction is that the topic should be suitable for 3rd year Bachelor students in compsci. I saw their curriculum and they have 3 Advanced math subject which is quite ambiguous because these subject often depend on the university and are not standardized. They also take a lot of mechanics, physics and other technical courses needing maths. Anyway, talking about my current research with these restriction is almost impossible. So I decided to mellow it down and to talk about one of these three subjects (as my research roughly belong in these area if you level it down too much):
Elliptic curves: I will try to roughly show them what elliptic curve groups over the real field (I dont expect them to know what finite fields are or to know much about groups and I think anyway its easier to define elliptic curve on the reals) is and give practical example like ElGamal or ECDSA
Sturms theorem on counting real roots of polynomial and possibly an algorithm. Very basic stuff but at least 20minutes is very manageable with this
Dijkstra in Graph theory and a practical example in say (robotic) path planning that uses Dijkstra.
Now among the dozen of people who will watch this only one is a mathematician (who works in stochastic which is absolutely not my field, he also seem to know cryptography), one is a computer scientist who seems to be interested in software design, 2 students (apparently compsci) and (since it is a college of applied science) two external people who belong to the (computer) industry.
The rests are either the HR team or the head of the college (they don't have voting rights on my placement).
I've never done this before. Applying to universities I often just get normal interviews from department chairs. I don't want to mess this up though. So a little advise would be nice. I was thinking ECC could be a bit too much for 20 minutes and maybe not advisable. Sturm's Theorem is almost a sure thing and a safe thing to choose whilst Dijkstra could be more interesting to compsci student but does not necessarily show my mathematical skills.
I hope this question is suitable for math.stackexchange and thanks for the advise in advance and wish me luck guys!