Representations of Galois groups of number fields encode symmetries among algebraic numbers. Wang-Erickson is interested in moduli spaces where each point corresponds to a p-adic Galois representation, and families in the space correspond to p-adically interpolated p-adic Galois representations. His projects have included efforts to refine the technologies used to understand and measure these spaces, which especially involve deformation theory and homotopical algebra. A particular goal is to identifying close relationships between arithmetic phenomena and deformations of Galois representations.