In a nutshell, we will study the fundamental subjects listed below. Everything treated in the lectures will be illustrated by detailed programming examples, which will be available. An interactive website (a "wiki") will allow students to actively participate in the course. Previous programming experience is not really necessary.
Direct Sampling. Markov-chain sampling, convergence issues, transfer matrices. Perfect sampling.
Molecular dynamics, and the relation to Markov chains. Direct sampling, Markov chain sampling: Algorithms Birth-and-death processes, perfect sampling. 2D melting transition, Kosterlitz-Thouless transition, entropic phase transitions.
Density matrices and path integrals. Superfluidity and condensate fractions: a path-integral point of view. Sampling of path integrals, from the Lévy construction to interacting path integrals. Ideal bosons from a path-integral perspective. Path integrals and the geometry of random manifolds. Roughness exponent, Fractional Brownian motion.
Ising Markov chains: local moves, cluster moves. Finite-size scaling. 2D XY model: Monte Carlo algorithms and hybrid approaches. Kosterlitz-Thouless physics. Perfect sampling: semi-order and patches. Sampling and exact solutions (in general) and the Onsager solution (in particular).