Seminarium KMMF "Teoria Dwoistości"

Supersolids have been the subject of much recent experimental work on ultra-cold Bose gases. In this talk I will explain the mathematical model behind it (the Gross-Pitaevskii equation) and state some recent rigorous results obtained in collaboration with P.T. Nam (Munich). I will explain how to mix tools from PDEs and statistical mechanics to study the phase diagram of this nonlinear equation. The main result is that there is a unique freezing transition for interaction potentials that are stable but not positive definite.