Professor Cazeaux's research in applied mathematics covers a range of subjects in mathematical modeling, rigorous analysis of partial differential equations and numerical simulations of multiscale phenomena arising from applications in materials science and biology.
Mathematical modeling, applied analysis, asymptotic regimes of partial differential equations and scientific computing are themes that play a central role in his work.
Analysis and numerical simulations of models at the quantum level of materials and molecules is an unending source of challenging, yet exciting mathematical problems. Two-dimensional materials are one such example, all the more interesting due to the incredible interest in the condensed matter community leading to interdisciplinary work opportunities.
As we make further progress in the computation of linear-response single-electron quantities such as the conductivity, the framework and numerical methods developed by Prof. Cazeaux and his collaborators will be the basis for further investigation into coupled electron-phonon behavior or nonlinear self-consistent field models such as Density Functional Theory calculations.