Geometric methods in quantum mechanics
May 17, 18, 24, 25, 2021
Prof. MAURO SPERA, Università Cattolica del Sacro Cuore
Since its emergence during last century's twenties, quantum mechanics has fostered the development of both old and entirely new mathematical domains, thus providing a perennial source of fascinating research problems. The present course, mainly geared towards (but not limited to) mathematicians, is intended as a gentle introduction to the mathematical aspects of quantum mechanics, focussing on the geometrical ones. Here is a cursory and tentative list of the planned topics: quantum mechanics (overview), geometric quantum mechanics, geometric quantization and applications, geometry of the Madelung-Bohm hydrodynamical approach, abelian varieties and theta functions. Basic acquaintance with differential geometry is required; however, specific technical tools will be introduced when needed.