Title: Ricci flow on surfaces with a view toward uniformization
Abstract: Ricci flow has famously been applied in three dimensions to prove the Poincare conjecture and shed new light on 3D geometry. In this talk, I will explore to what extent these new tools may be applied to the classical problem of geometry in two dimensions. Many of the theorems initially proved in the turn of the 20th century can now be approached from the methods of Ricci flow. That we can derive such results from the Ricci flow indicates that it is in fact interesting in all dimensions and, indeed, the 4D case is now being pursued at the cutting edge of research.