I am a professor working on condensed matter theory. My current interest is in topological order, which correspond to patterns of long-range entanglement in many-body system.
Understanding patterns of many-body entanglement is related to some modern mathematics. For example, the mathematical foundation for 2D long-range entanglements happen to be unitary modular tensor category theory. For higher dimensions, we may need unitary braided fusion higher categories. The mathematical framework for short-range entanglements with symmetry happen to be group cohomology theory of the symmetry group and cobordism theory.