A short geometric proof of the Zalcman and Bieberbach conjectures
  We show that complex geometric features of Teichmuller spaces create explicitly the extremals of generic homogeneous holomorphic functionals on univalent functions. In particular this gives proofs of the well-known Zalcman and Bieberbach conjectures and many new distortion theorems. 
Samuel L. Krushkal
math.CV