Grant: Discovery Grants Program - Individual

Ever since the introduction of quantum mechanics, the question of how to relate the classical and quantum descriptions of a system has been an ongoing issue, one which is not satisfactorily resolved even today. I am interested in the question of how classical mechanics relates to quantum mechanics, from the mathematical point of view. ""Quantization'' refers to the mathematical process of passing from the classical description of a system to a quantum mechanical one; one such process is geometric quantization, where the geometry of the classical system is used to define the corresponding quantum object. Some aspects of the theory are well-developed, but there are a number of open questions that remain. In particular, I will study ways of extending the methods of geometric quantization to systems to which the existing theory does not apply, such as systems with singularities.