Geometric complexity theory
Geometric Complexity Theory, often shortened to GCT, is a research program in computational complexity theory proposed by Ketan Mulmuley. The goal of the program is to answer the most famous open problem in computer science P vs. NP by showing that the complexity class P is not equal to the complexity class NP.
The idea behind the approach is to adopt and develop advanced tools in algebraic geometry and representation theory to prove lower-bounds for problems. Currently the main focus of the program is on algebraic complexity classes. Proving that Permanant cannot be efficiently reduced to Determinant is considered to be a major milestone for the program. These computational problems can be characterized by their symmetries. The program aims at utilizing these symmetries for proving lower-bounds.
The approach is often considered the only viable currently active program to separate P from NP. However, according to Mulmuley the program is likely to take hundreds of years before it can settle the P vs. NP problem.
The program is pursued by several researchers in mathematics and theoretical computer science. Part of the reason for the interest in the program is the existence of arguments for the program avoiding all known barriers for proving general lower-bounds.