Introduction to nonlinear Schrödinger equations

In this talk, I will give an introduction to the existence theory of nonlinear Schrödinger equations. Nonlinear Schrödinger equations (NLS) arise in physics in the study of Bose-Einstein condensation and nonlinear optics. They provide an important example for semilinear dispersive evolution equations and have received much attention over the past decades for their interesting mathematical effects such as blow-up of solutions, existence of solitons, and scattering. I will talk about local and global existence of solutions to NLS and present my own work in this direction with Paolo Antonelli (SNS, Pisa) and Christof Sparber (UIC, Chicago).