Jan Philip Solovej
University of Copenhagen, Denmark

I will give an overview of the mathematical description of quantum many-body systems, in particular, the ground states of gases of many interacting identical particles. Such systems can be experimentally implemented in (very) cold atomic gases. The atoms are either bosons (e.g. Lithium7) or fermions (e.g., Lithium6). Bosons in three dimensions at very low temperature form Bose-Einstein condensates (although we do not know how to show this rigorously) and become superfluid. I will discuss recent rigorous results on the pressure of three dimensional Bose gases in the limit when they become dilute. The formula is in agreement with the theory of superfluidity and thus validates aspects of the theory. I will also review what is known in other dimensions and for Fermi gases. This is based on work with my former students Agerskov, Fournais, and Reuvers.