Title: Low regularity solutions of Chern-Simons-Schroedinger System

Abstract:
The nonrelativistic Chern-Simons model arise in the physics of high
temperature superconductivity or second-quantized N-body anyone
problem. Mathematically, it is a covariant NLS-type problem that is L2
critical. In this talk, I will introduce the so-called heat gauge
which seems to be well-adapted to our problem.  By exploring the null
structure in the nonlinearity and applying bilinear estimates in finer
scale, we obtain local wellposedness for initial data which is small
in $H^s$, for s>0.

This is joint work with Paul Smith and Daniel Tataru.