I often get asked what type of mathematics I do, or what mathematicians do in general. So I thought I'd give as much of an explanation as I can, assuming as little background knowledge as possible. This is of course a single example amongst a topic that has existed in every human culture throughout history, but this box inside a drawer inside the cupboard inside the room inside the house inside the city inside the country inside the world of mathematics is one I've spent a lot of time in.
The formal title of my work is "Polynomial and combinatorial analogues of Gauss congruences". We'll get to what all of these words mean eventually! For a one-sentence summary: we study mathematical objects similar to necklaces through their rotational symmetries.
In general we will be working in the field known as combinatorics. In short, this is the area of mathematics concerned with counting things. For example, how many ways are there to scramble a Rubik's cube? (43,252,003,274,489,856,000, which is a lot)