The Brown Research Group aims to study single-, few-, and many-body quantum physics by conducting quantum simulation experiments. Quantum simulations are realizations of complex quantum systems for the purpose of understanding their ordered phases and dynamics. His group traps ultracold atoms in optical lattice potentials (an ultracold atom quantum simulator), which is the spatially periodic potential the atoms experience in the intensity standing wave of several intersecting lasers. In doing so, the Brown group aims to learn about exotic ordered phases of ultracold bosons and fermions in optical lattices, how transport works in lattices with unusual geometry (e.g., a “lattice” that lacks translational symmetry), and what role topology plays in the quantum behavior of bosons and fermions in such unusual lattices.