A finite number of people want to cut up a piece of cake amongst themselves `fairly'. How efficiently can they do this? Almost everything is known in the case where each of the $N$ people want $1/N$ of the cake. On the other hand, the more general problem where each person wants an arbitrary real fraction of the cake is rather poorly understood. In this talk, we shall improve considerably on classical, decades-old arguments from algebraic topology and report on an efficient, combinatorial procedure for the general problem that yields nearly optimal bounds.
Joint work with Logan Crew and Sophie Spirkl.