Conformal Deformation on Manifolds with Boundary
  We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly from C^0 estimates for fully nonlinear equations. The main result has appeared in the author's thesis. 
Szu-yu Sophie Chen (IAS and Berkeley)