We consider unbounded fanin depth-2 circuits with *arbitrary*
boolean functions as gates. We define the entropy of an operator
$f:\{0,1\}^n \to\{0,1\}^m$ as the logarithm of the maximum number
of vectors distinguishable by at least one special subfunction of f.

Main result: Every depth-2 circuit for f requires at least  entropy(f) wires. 

This is reminiscent of Nechiporuk's lower bound on the  formula size, 
and gives an information-theoretic explanation of why some  operators require many wires.  

As a direct corollary this implies that $n^3$ wires are necessary
to multiply two nXn matrices using depth-2 circuits with arbitrary gates.
Previously known lower bound for this operator was $n^2\log n$.

(iii) Talk duration: about 30-40 minutes.

(iv) Can be given the first day.