Mathematical Conversations
Many interacting quantum particles: open problems, and a new point of view on an old problem
The main object of interest in this talk will be a system of many particles, modeled using the prescriptions of quantum mechanics. A significant challenge to studying such systems is that particles interact with each other, via weak or strong, attractive or repulsive forces, which induce correlations, and make it so that, to understand the properties of the system, one must understand the behavior of all particles at once. In this talk, I will consider one of the simplest interacting quantum systems, called the "Bose gas", and I will review what is known, and discuss a collection of open questions. Finally, I will discuss an approach to this model, which may seem odd at first glance, but which seems to be very successful to understand the properties of the interacting Bose gas in a way that is conceptually and computationally simple.