I will discuss the problem of finding a planted bipartition in a random k-uniform hypergraph (the hypergraph version of the stochastic block model). The problem exhibits an algorithmic gap: while the partition is detectable with a linear number of hyperedges, the best known efficient algorithms require up to n^{k/2} hyperedges. I'll present a general framework for proving computational lower bounds for the class of statistical algorithms on problems over distributions and apply it to the planted partition problem to achieve nearly matching upper and lower bounds. Based on joint work with Vitaly Feldman and Santosh Vempala.