The Geometric Complexity Theory (GCT) program was introduced by Mulmuley and
Sohoni to attack fundamental lower bound problems in complexity - such as P vs
NP - using algebraic geometry and representation theory. In addition to presenting
the basic structure of the GCT program, I will discuss some of the  intuition
behind the use of algebraic geometry and representation theory in complexity.
This is an expository talk; the only mathematical background presumed is a basic
familiarity with group actions and polynomial rings.