Mathematical Models of Electronic Transport and Phases in Low-Dimensional Materials

March 11, 2024 - March 15, 2024


Svetlana Jitomirskaya
UC Irvine
Mitchell Luskin
University of Minnesota
Allan H. Macdonald
University of Texas, Austin
Dionisios Margetis
University of Maryland

Low-dimensional moiré materials provide a rich testing bed for exploring novel quantum phenomena of electronic transport. For example, twisted bilayer graphene has attracted much attention because of the electronic phases that emerge for twists near the "magic angle". Novel predictions include unconventional superconductivity, correlated insulators, anomalous quantum Hall ferromagnetism, and intriguing viscous hydrodynamics.

The physically inspired models lead to far-reaching mathematical questions about limits of quantum particle systems, the modeling of dissipation and electronic viscosity, the topology of energy bands, quasi-periodic Schrödinger operators, semi-classical limits, and the linear and nonlinear optical response, among others. The underlying areas of mathematics span partial differential equations, topology, numerical analysis, and statistical mechanics.

The goal of this interdisciplinary workshop is to bring together mathematicians, and theoretical and applied physicists with the purpose of identifying and discussing new mathematical problems of physical importance in electronic transport.