Novel results from an algebraic approach to molecular bending dynamics

We present a brief review of research topics of current interest that depend on an algebraic approach to molecular bending dynamics. This approach is based on a u(3) spectrum generating algebra. In particular, we briefly present results on three topics: the calculation of finite-size analytical corrections to mean field results, the application of the model to the largeamplitude vibrational bending mode of the NCNCS molecule, and the analysis of the influence of quadratic Casimir operators on excited state quantum phase transitions