We plan to cover one of the most significant result in the area
of arithmetic circuit complexity, namely "Depth-4 chasm" due to Agrawal,
Vinay 2008. It greatly simplified the work of researchers to focus only on
depth <= 4 arithmetic circuits for the purpose of lower bound and
polynomial identity testing problems. We will cover the proof in 2 steps.
We will start by reducing a general circuit to O(log d) depth, where d is
the degree of the polynomial the circuit is computing. This result is due
to Valiant et cetera 1983. The second step would be to convert this new
circuit to depth-4 along the lines of AV08.