Title:  Oracles Are Subtle But Not Malicious

                   Scott Aaronson
		Institute for Advanced Study (IAS)

Abstract:  I'll first review the concept of an oracle, and why it plays such
a central role in the P/NP question and in theoretical computer science more
generally.  I'll then survey the slim progress that's been made so far
toward proving nonrelativizing lower bounds.  Finally I'll present a new
result: that there exists an oracle relative to which the computational
complexity class PP (Probabilistic Polynomial-Time) has linear-size
circuits.  The reason this is interesting is that Vinodchandran showed, via
a nonrelativizing argument, that PP does *not* have circuits of size n^k for
any fixed k.  Indeed I've extended Vinodchandran's result, to show that PP
does not even have quantum circuits of size n^k with quantum advice.

Prerequisites: You don't need to understand http://www.complexityzoo.com;
you just need to be able to stare at it for at least 15 seconds without
screaming in terror.

More details: http://arxiv.org/abs/cs.CC/0504048

Notes for a related talk: http://www.scottaaronson.com/talks/subtletalk.pdf