My most recent works have focused on twisted bilayer graphene (TBG): two layers of the 2D material graphene, stacked with a relative interlayer twist. The atomic structure of TBG is aperiodic for generic twists, but nevertheless has approximate large-scale periodicity known as the bilayer moiré pattern.
In publication 11 (see Publications), I rigorously justified the Bistritzer-MacDonald PDE model, which captures the electronic properties of TBG on the moiré scale and allows for computation of an approximate band structure/dispersion relation for electrons in TBG. This model led to predictions of many-body quantum phases such as superconductivity at the "magic" twist angle 1°, which were recently experimentally observed.
My PhD advisor at Columbia was Michael I. Weinstein. I was William E. Elliott Assistant Research Professor at Duke working primarily with Jianfeng Lu, and then Postdoctoral Associate at UMN working primarily with Mitchell Luskin.
Right: the dispersion relation for electron propagation in TBG; first without, and then with, interlayer tunneling turned on. Interlayer tunneling causes the Dirac cones of monolayer graphene to form nearly-flat bands, leading to many-body quantum phases such as superconductivity at the "magic" twist angle 1°. Figure by Tianyu Kong.