  In this short note, we describe a problem in algebraic geometry where the
solution involves Catalan numbers. More specifically, we consider the derived
category of coherent sheaves on an elliptic surface, and the action of its
autoequivalence group on its Bridgeland stability manifold. In solving an
equation involving this group action, the generating function of Catalan
numbers arises, allowing us to use asymptotic estimates of Catalan numbers to
arrive at a bound for the solution set.
