Matrix models of noncommutative geometry and string theory

Feynman path integrals and phase transitions in quantum field theory.

The Ising model and commutative scalar phi-four theory.

String theory in 2 dimensions as discretized surfaces and random matrices.

The large N saddle point and orthogonal polynomial methods.

The $\theta=0$ and $\theta=\infty$ limits of noncommutative field theory.

The multitrace expansion of noncommutative scalar field theory.

Monte Carlo algorithms for matrix models.

The phase structure of noncommutative phi-four.

The IKKT matrix model and non-perturbative superstring theory.

Yang-Mills matrix  models of noncommutative gauge theory. 

BFSS matrix quantum mechanics, M-(atrix) theory and the gauge/gravity duality.

Yang-Mills matrix quantum mechanical models.

Large $d$ expansion of Yang-Mills quantum mechanics.

Emergent geometry and noncommutative gauge theory  in Yang-Mills matrix models.

AdS/CFT correspondence in two dimensions and noncommutative geometry.

Wilson renormalization group equations for matrix and noncommutative models.

Noncommutative quantum black holes.

Emergent gravity and quantized symplectic geometry.

Matrix cosmology and emergent time in IKKT and BFSS matrix models.