The Edinburgh Mathematical Physics Group (EMPG) was founded in 1999 by mathematical physicists at Edinburgh and Heriot-Watt universities.

Since that time the EMPG has grown in size to the present 10 FTE academic members of staff. In addition, the EMPG benefits from the presence of two distinguished research-active honorary professors (Michael Atiyah and Oliver Penrose). The main research areas covered by the group are the following:

- Gravitational physics and AdS/CFT: Holography, duality and supersymmetry are theoretical physics concepts attempting to bridge the gap between Quantum Theory and General Relativity. Our research focuses on the geometry of supersymmetry and supergravity, the classification of gravitational solutions in various dimensions, black holes and their applications to the AdS/CFT duality, and the development of holography in more general spacetimes.
- Two-dimensional conformal field theory and renormalisation group flows, worldsheet methods in string theory.
- Noncommutative geometry and field theory, K-theory, and algebraic geometry, together with their applications in string theory, quantum field theory, and quantum gravity; higher algebraic and geometric structures in string theory and M-theory; four-dimensional geometry.
- Integrable systems and statistical mechanics: twistor descriptions of classical integrability in the context of M-theory, statistical mechanical models, exact algebraic and combinatorial descriptions of quantum integrable models and their application to quasi-one-dimensional systems, the mathematics of integrable systems arising from diverse contexts such as monopoles, Seiberg-Witten theory, and sigma-models; solvable models in non-equilibrium statistical mechanics, Monte Carlo simulations of lattice spin models and discretized models of gravity, applications of information geometry to phase transitions.