Chapter 5: Understanding Quantum Physics: Why Geometry and Algebra Matter

This short contribution is a review of some of the scientific results that were achieved in Syracuse during my stay as a PhD student under the supervision of A.P. Balachandran from 1990 to 1994. It was an exciting period during which we worked closely with other PhD students and many visiting researchers on the mathematical structures of quantum mechanics. The research focused on some fundamental issues that the physical community managed to understand but put in a full coherent theory only much later.