Clare Dunning Department of Mathematics, The University of Queensland Insights into PT-symmetric quantum mechanics via integrable models Wednesday 23th, March 14:05-14:55pm, Carslaw Building Room 373. In standard quantum mechanics the Hamiltonian is Hermitian and as a consequence the spectrum is real and time evolution is unitary. Recently, Bender has proposed that Hermiticity may be replaced by the weaker (and more physical) condition of space-time reflection symmetry (PT-symmetry) without losing key properties of the models. Using tools from an intriguing connection with integrable models, we prove that a certain class of PT-symmetric (and non-Hermitian) Schrödinger problems have an entirely real and positive spectrum.