Bio: Mitchell Luskin is a Mathematics professor at the University of Minnesota’s School of Mathematics. He develops mathematical models and computational methods with applications to physics and mechanics. His current research focuses on quantum materials, machine learning, and data-enabled modeling.

Luskin’s early work proposed and analyzed finite-difference and finite-element methods for fluid dynamics, normal modes of the oceans, neutron transport, and viscoelasticity. Later work developed methods for liquid crystal defects and for materials with microstructure. More recent work formulated atomistic-to-continuum coupling and accelerated molecular dynamics methods

Research Interests:

• Numerical analysis
• Scientific computing
• Applied mathematics
• Computational physics

Math and Physics at the Moiré Scale

Placing a two-dimensional lattice with a small rotation gives rise to almost periodic “moiré” patterns on a superlattice scale much larger than the original lattice. We have used the mathematical techniques developed to study waves in inhomogeneous media to identify a regime where the Bistritzer-MacDonald continuum model emerges as the effective dynamics for electrons modeled as wave-packets spectrally concentrated at the monolayer Dirac points of linear dispersion, up to error that we rigorously estimate. We have shown that this regime is realized in twisted bilayer graphene at the first “magic" angle where the group velocity of the wave packet is zero and strongly correlated electronic phases (superconductivity, Mott insulators, etc.) have recently been observed.

We will present recent results that rigorously extend this analysis to account for the effects of structural relaxation and to essentially arbitrary moiré materials such as twisted multilayer transition metal dichalcogenides (TMDs) or even twisted heterostructures consisting of layers of distinct 2D materials.

The MICDE 2026-27 Seminar Series is open to all.

Graduate Certificate in Computational Discovery and Engineering and MICDE fellows, please use this form to record your attendance.

Questions? Email [email protected]