  Let $a$ and $b$ be two coprime positive integers and $k$ an arbitrary field.
We determine the ring structure of the Hochschild cohomology of the numerical
semigroup algebras $k[s^{a},s^{b}]$ of embedding dimension two (thus also
complete intersections) in terms of generators and relations. In addition, we
compute the Hilbert series for this cohomology ring.
