Part IX: From Perelman to the Standard Model

Gauge geometry, RG flow & infrared memory — how the mathematics of Ricci flow, spin memory, and the Standard Model share a common variational and geometric skeleton.

This module extends the Lagrangian connections of Part VIII to the full Standard Model of particle physics. The Yang–Mills Lagrangian is shown to be the gauge-theoretic analogue of the Einstein–Hilbert action; Yang–Mills flow parallels Ricci flow; the beta functions of QED, QCD, and electroweak theory are RG flows on gauge coupling space; soft photon and gluon theorems have their own infrared triangles and memory effects; instantons perform “topological surgery” analogous to Perelman's neck-pinch surgery; and the BV–BRST cohomology of the Standard Model extends the gravitational infrared triangle to all four forces.