Unification: Geometry, Gauge Theory & Quantum Gravity

The quest for a unified theory of all fundamental forces — from string theory and M-theory through loop quantum gravity to the geometric connections between Perelman's Ricci flow, BMS symmetries, and the Standard Model.

This course explores the major approaches to quantum gravity and unification, with full mathematical derivations. Part I covers string theory from the bosonic string to superstring dualities. Part II develops M-theory, D-branes, and the AdS/CFT correspondence. Part III surveys alternative approaches: loop quantum gravity, spin foams, causal sets, asymptotic safety, and emergent gravity. Part IV connects everything through the geometric framework developed in the GR course — Perelman's Ricci flow, the spin memory effect, Lagrangian connections, and the extended master Lagrangian.