Approximation theorems for the Schrödinger equation and the reconnection of quantum vortices in Bose-Einstein condensates (Joint w/ IP seminar) 

 Abstract:  The Gross--Pitaevskii equation is a nonlinear Schrödinger
equation that models the behavior of a Bose-Einstein condensate. The
quantum vortices of the condensate are defined by the zero set of the
wave function at time $t$. In this talk we will present recent work
about how these quantum vortices can break and reconnect in
arbitrarily complicated ways. As observed in the physics literature,
the distance between the vortices near the breakdown time, say t=0,
scales like the square root of t: it is the so-called $t^{1/2}$ law.
At the heart of the proof lies a remarkable global approximation
property for the linear Schrödinger equation. The talk is based on
joint work with Daniel Peralta-Salas.