Recent developments in lattice effective field theory

The talk contains two parts. Part 1: The adiabatic projection method is an ab initio technique for constructing an effective cluster Hamiltonian using lattice Monte Carlo. I discuss recent applications of the adiabatic projection method, including first principles simulations of alpha-alpha scattering using lattice effective field theory. Part 2: Impurity lattice Monte Carlo is a hybrid algorithm which uses worldline simulations for an impurity and auxiliary-field simulations for the many-body fermionic environment. I discuss recent applications of impurity lattice Monte Carlo to the two-dimensional attractive polaron problem.