What does elementary school addition have to do with cohomology? To add two-digit numbers, you need to know how to add one-digit numbers and the carrying rule. In this talk, I'll explain how this is an example of a group extension: a way of building a larger group out of two smaller groups. By abstracting properties of the usual carrying rule, we'll come across some other extensions which correspond to funky new ways of adding two-digit numbers. Amazingly, the collection of all these extensions forms a group itself, which turns out to coincide with a particular cohomology group! If time permits, I'll expound the power of this unexpected application of cohomological methods to finite group theory.
No background is necessary aside from basic group theory and familiarity with addition.