On the Singularities of the Exponential Map in Infinite Dimensional   Riemannian Manifolds
  Using symplectic techniques and spectral analysis of smooth paths of self-adjoint operators, we characterize the set of conjugate instants along a geodesic in an infinite dimensional Riemannian Hilbert manifold. 
L. Biliotti, R. Exel, P. Piccione, D. V. Tausk