# Special CMX Seminar

*,*Professor

*,*Department of Mathematics

*,*University of Minnesota

*,*

Mitchell Luskin is a professor of mathematics at the University of Minnesota who is working to develop computational methods to accurately and efficiently simulate complex physical systems at large length and time scales. His interests include methods that couple atomistic to continuum models and accelerated molecular dynamics. At Radcliffe, Luskin is developing multiscale mathematical and computational methods to model the electronic and mechanical properties of two-dimensional materials. His work focuses on the mathematical modeling of weakly interacting single atom layers of semimetals (graphene), insulators, and semiconductors. These materials pose a challenging yet accessible test-bed physical system for the further development of multiscale methods. The development of predictive models for two-dimensional layered materials will open the possibility of computationally searching all possible ways to combine single atom layers and thus design materials with desirable, tailor-made electronic, optical, thermal, and mechanical properties. Luskin received a BS in mathematics from Yale College and a PhD in mathematics from the University of Chicago. He has recently been a distinguished Romberg Guest Professor at the University of Heidelberg and a visiting scholar at Pembroke College Cambridge. He is a fellow of the American Mathematical Society and the Society for Industrial and Applied Mathematics.

Stacking and twisting a few layers of 2D materials such as graphene opens the possibility of tuning the electronic and optical properties of 2D materials. One of the main issues encountered in the modeling of 2D heterostructures is that lattice mismatch and rotations between the layers destroys the periodic character of the system. I will present basic concepts and efficient computational methods for mechanical relaxation, electronic density of states, and conductivity in the incommensurate setting.

Superconductivity has recently been discovered in twisted bilayer graphene at a "magic" twist angle with an isolated "flat band." I will describe our search for superconductivity in twisted trilinear graphene in collaboration with the experimental group of Ke Wang by computing its mechanical relaxation and the spectrum (band structure) of its Hamiltonian.