| Abstract: | Layering two-dimensional periodic materials to form moiré structures is a convenient method of constructing emergent periodicity with on-demand length scales. This scheme has proven fruitful for engineering new electronic structures hosting superconductivity, strong electronic interactions, and topology. In contrast, quasicrystals, without periodicity or a Bloch description, have proven more challenging to engineer and thus are much less explored. In my talk, I will demonstrate how moiré lattices can be used to generate emergent quasiperiodicity with both a high degree of tunability and conditions favorable for interacting electronic phenomena. I will discuss a graphene-based realization of a moiré quasicrystal that exhibits a wide array of phenomena, including superconductivity, flavor symmetry-breaking, quantum oscillations, and signatures of both periodic-like and quasiperiodic regimes in the electronic structure |