Summary
The investigator studies problems in spectral theory, the mathematical theory that pertains to physical notions such as energy levels of quantum systems and vibration frequencies of mechanical systems. The research is motivated by universality, which is the appearance of certain common local statistical behaviors for different systems, and integrability, which is the existence of many conserved quantities in certain nonlinear systems used to describe their behavior over time. The project focuses on commonly studied one-dimensional systems, such as orthogonal polynomials and Schrödinger operato
