The physics of ultracold quantum gases and Bose-Einstein condensation is currently a very active field of both experimental and theoretical research worldwide. Unveiling the fascinating properties of such quantum many-body systems by rigorous mathematical analysis is an important and difficult challenge for mathematical physics. Considerable progress has been made in recent years involving a variety of mathematical techniques, such as spectral theory of partial differential operators with a large number of variables, nonlinear partial differential equations, random walks on lattices and functional integration. Several of the most basic basic questions are still unanswered, however, and there is much to be learned. The workshop will bring together experts with different backgrounds to review the current status of mathematical results in the field and to discuss new developments where a mathematical approach is potentially fruitful.