The key concept in the physics of materials is that “More is different”, meaning that a macroscopic number (~10^23) of electrons leads to fundamentally new, emergent behavior, not imaginable for single electrons. A central theme is emergence of electronic ordering, with the paradigm examples of magnetism and superconductivity. Ordering requires interactions between electrons and is also heavily dependent on the density of states (DOS) at zero energy: the more zero-energy DOS, the more likely electronic ordering. Our research primarily focuses on superconductivity, a uniquely quantum mechanical ordered state. We are currently pursuing multiple different projects, all focusing on enhancing and understanding superconductivity. We aim to theoretically create and enhance superconductivity by producing large DOS peaks at zero energy using nanoscale inhomogeneity. Examples of nanoscale inhomogeneity are moiré structures, such as in twisted bilayer graphene an all-carbon material hosting large zero-energy DOS peaks due to the twist recently shown to create superconductivity, certain types of disorder, which also generate multifractal behavior, and superconducting phase crystals, where the superconductor itself creates the inhomogeneity due to zero-energy DOS peaks. A material is usually also coupled to an outside environment, turning it into an open system. For quantum phenomena this often means more classical behavior, and electronic ordering is naively expected to be much less likely in strongly open systems. Many effects of openness can be effectively treated by introducing non-Hermitian (NH) terms in the otherwise normal, or Hermitian, Hamiltonian (energy operator) describing the material. One central NH effect is the existence of exceptional points (EPs), where not only the (eigen)energies are degenerate but the wavefunctions (eigenvectors) also become parallel. We aim to use EPs at zero energy to create both the necessary large DOS for ordering, especially superconductivity, and fundamentally different behavior due to their unique wavefunctions. Finally, we study effects of topology on quantum systems, especially topological superconductivity, uniquely advantageous for quantum computing. Topological superconductors can have effective Majorana fermions at surfaces, vortices, and other defects. One can say that a Majorana fermion is half an electron, or more accurately, in a system with Majorana fermions the wave function of an electron has split up into two separate parts. It is this non-local property that can be used for fault-tolerant quantum computing. We aim to theoretically discover new topological superconductors and determine the properties of the Majorana fermions.