GCT: Algebraic Geometry Links P vs NP to Orbit Closures — E8 Intelligence Research

FINDING: Geometric Complexity Theory (GCT) reformulates P vs NP as a problem of symmetry and representation theory, linking algebraic geometry to computational complexity via orbit closures and plethysm coefficients. | MATH: Key objects: orbit closures of determinant (Det_n) and permanent (Perm_m) under group actions (GLn^2 × GL_n). The central conjecture: Perm_m is not in the orbit closure of Det_n for m >> n, implying VP ≠ VNP (algebraic analog of P ≠ NP). This reduces to non-vanishing of certain multiplicities in plethysm decompositions of coordinate rings. No explicit constants or ratios appear; the core is representation-theoretic: Kronecker coefficients, Littlewood-Richardson coefficients, and their asymptotic behavior. | CONNECTION: The symmetry groups involved (GL_n, S_n) are intimately tied to root systems of type A_n, whose Weyl groups are symmetric groups. The orbit closure geometry mirrors the structure of flag varieties and Schubert calculus, which exhibit crystallograp Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com