Geometric evolution equations and the Poincare conjecture
 
           Ben Andrews (Australian National University)
 
In this series of lectures I will describe the recent work by Perelman,
in which nonlinear heat equations are applied to prove the
Poincare conjecture (and, probably, Thurston's geometrisation conjecture).
 
Lecture 1:  Introduction to the Poincare conjecture
 
The first lecture will be a survey, covering the background of the
Poincare conjecture.  I will discuss some of the convoluted history
of the problem, including some of the famous
false starts and counterexamples.
 
Lecture 2:  Introduction to geometric evolution equations
 
In the second lecture I will give an overview and history of geometric
evolution equations, leading up to Richard Hamilton's program to use the
Ricci flow to prove Thurston's geometrisation conjecture.

Lecture 3:  Perelman's argument
                                                                                
In the final lecture I will discuss the enormous advances Perelman has
made and the outline of his proof.