Geometric complexity theory

Geometric complexity theory is an approach towards proving lower bounds in algebraic complexity theory via methods from algebraic geometry and representation theory. It was introduced by Mulmuley and Sohoni and has gained significant momentum over the last few years.

Geometric complexity theory is an ambitious program initiated in 2001 by Mulmuley and Sohoni towards solving the famous P vs NP problem. The idea is to use algebraic geometry and representation theory to prove complexity lower bounds for explicit problems.