Exact Results in Quantum Theory

Since the experimental realization of Bose-Einstein condensation (BEC) in Bose gases, it has been an ongoing challenge in mathematical physics to derive the phenomenon from the first principles of quantum mechanics. This has first been achieved in 2002 by Lieb and Seiringer for dilute, trapped systems. More recently, BEC has been proven for weakly interacting systems within the so-called mean-field limit. In my talk, I will both review existing and present recent results on the dynamics of weakly interacting Bose gases in the mean-field limit.