After a quick glance at your website, I think you should definitely talk about symmetry and invariants and any tie-in to cryptography.

The general audience loves visual symmetry and you may actually be able to describe some of the higher order symmetries you investigate through basic analogy.

Invariants are also a great topic that I think would be accessible, but that few people might have thought about. In a way, invariants are like the physical laws of conservation (of energy, momentum, etc.). There are some great accessible problems that use invariants (usually of the flavor: notice that in this set-up these two quantities always have to sum to an even number, thus it's impossible for one to be even and the other odd). That type of thinking is so natural to mathematicians, but often very foreign to others. Yet once they see it, they immediately appreciate it.

You could then tie this into cryptography. Surely there are some neat schemes out there that rely on symmetry, seem very convincing, but are broken under some sort of invariant calculation. The talk could progress as: Crypto Scheme, Why it works (via symmetry), The Power of Invariants, How it can be broken. (I've seen very accessible talks in this vain as an intro to basic linear algebra.)

Good luck!

After a quick glance at your website, I think you should definitely talk about symmetry and invariants and any tie-in to cryptography.

The general audience loves visual symmetry and you may actually be able to describe some of the higher order symmetries you investigate through basic analogy.

Invariants are also a great topic that I think would be accessible, but that few people might have thought about. In a way, invariants are like the physical laws of conservation (of energy, momentum, etc.). There are some great accessible problems that use invariants (usually of the flavor: notice that in this set-up these two quantities always have to sum to an even number, thus it's impossible for one to be even and the other odd). That type of thinking is so natural to mathematicians, but often very foreign to others. Yet once they see it, they immediately appreciate it.

You could then tie this into cryptography. Surely there are some neat schemes out there that rely on symmetry, seem very convincing, but are broken under some sort of invariant calculation. The talk could progress as: Crypto Scheme, Why it works (via symmetry), The Power of Invariants, How it can be broken. (I've seen very accessible talks in this vein as an intro to basic linear algebra.)

Good luck!