This research project is concerned with the mathematical analysis of quantum many-body systems. Important progress was already made during the course of the project. In a joint work [1] with Andreas Deuchert and Jakob Yngvason (University of Vienna), dilute trapped Bose gases were investigated at non-zero temperature. For gases in a harmonic trap, occurrence of Bose-Einstein Condensation was rigorously proved to occur in the Gross-Pitaevskii limit, generalizing previous results applicable only to zero temperature. This result was then extended to homogeneous systems [19], again in joint work with A. Deuchert. The Statistical Mechanics of a uniform electron gas was investigated in joint work [3] with Mathieu Lewin (Paris) and Elliott Lieb (Princeton University), establishing the existence of the thermodynamic limit in a very general sense. The validity of the local density approximation was then proved in the later work [preprint, arXiv:1903.04046]. In joint work with Niels Benedikter, Phan Thanh Nam (LMU Munich), Marcello Porta (Tübingen) and Benjamin Schlein (Zürich), the correlation energy of weakly interacting Fermi gases was investigated [23], and the Gellmann-Bruckner formula was shown to be asymptotically valid as an upper bound. The stability of fermionic systems interacting with point interactions is the subject of the joint work [2,5,6] with Thomas Moser (also at IST Austria). The validity of the Lieb-Thirring inequality for an ideal anyon system in two dimensions was proved in joint work [4] with Douglas Lundholm (KTH Stockholm). Moreover, Andreas Deuchert, Nikolai Leopold and myself have contributed in various ways [7,8,9,15] to the analysis of the angulon model describing rotating impurities in a quantum environment. The strong coupling limit of the polaron is the subject of publications [18,25,26]. The low-density asymptotics of the free energy of a two-dimensional Bose gas was established in [20,31]. Finally, a rigorous derivation of Haldane pseudo-potentials for dilute quantum gases in a magnetic field was obtained in [14].
