Rod Halburd Department of Mathematics, University College London Movable Algebraic Singularities of Solutions of ODEs Wednesday 8st April 14:05-14:55pm, Eastern Avenue Lecture Theatre. A class of second-order rational ordinary differential equations admitting certain families of formal algebraic series solutions is considered. For all solutions of these equations, it is shown that any movable singularity that can be reached by analytic continuation along a finite length curve is an algebraic branch point. The existence of these formal series expansions is straightforward to determine for any given equation in the class considered.