A simple proof of the $A_2$ conjecture

The $A_2$ conjecture says that the $L^2(w)$ operator norm            
of any Calder\'on-Zygmund operator is bounded linearly by the $A_2$  
constant of the weight $w$.                                          
This conjecture was completely solved in 2010 by T. Hyt\"onen.       
The proof was based on a rather difficult representation of a general
Calder\'on-Zygmund operator in terms of the Haar shift operators.    
In this talk we shall discuss a recent simpler proof completely      
avoiding the notion of the Haar shift operator.