Mathematics of Quantum Matter and Quantum Processes

This is a research project on the mathematics of quantum matter and quantum processes. The vision is to understand the fundamental properties of atoms, molecules and larger quantum many-body systems as well as quantum processes. One goal is a mathematical understanding of complex atoms and, in particular, the structure of the periodic table. Another objective is a mathematical analysis of larger systems, e.g., systems that exhibit quantum phenomena such as superfluidity or superconductivity. While it is fundamental to understand quantum matter, it is equally crucial to understand how states of quantum matter are processed. The focus is on processes that preserve certain symmetries of states. The aim is to delineate the geometry of the sets of such processes with the objective to optimize processes for different tasks or to find quantum communication channels with optimal capacities.