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Title: Algebraic symmetries of the hydrogen atom

Abstract: In this talk I will explain how the hidden symmetries of the hydrogen atom are organized via algebraic families of groups.  I will show how solutions of the Schrödinger equation of the hydrogen atom form an algebraic family of Harish-Chandra modules.  Time permits, I will present a new algebraic model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null-cone. No prior knowledge in quantum mechanics will be assumed.