# The V AMMCS International Conference

## Waterloo, Ontario, Canada | August 18-23, 2019

# AMMCS 2019 Plenary Talk

## Molecular-scale modeling and simulation of materials

### Eric Cances (Ecole des Ponts ParisTech)

Molecular-scale modeling and simulation is one of the most dynamics area of scientific computing. It has a very broad field of applications, ranging from chemistry and drug design to solid-state physics, materials science and nanotechnology.

It is also a inexhaustible source of exciting mathematical and numerical problems of various nature: linear and nonlinear partial differential equations, optimization and control, stochastic processes and Monte Carlo methods, spectral theory, group theory, non-commutative algebra and geometry, statistical methods and machine learningâ€¦

In this talk, I will give an overview of some mathematical models and numerical methods used to predict macroscopic properties of a material from its atomic structure. I will first present the case of perfect crystals, where e.g. band structure diagrams constructed from Bloch-Floquet theory allow us to understand the difference in behavior between conductors, semiconductors, and insulators, as well as some of the properties of emerging topological materials. I will then discuss recent advances in the challenging field of modeling and simulating disordered systems such as crystals with defects, doped semiconductors, glasses, quasicrystals, or multilayer 2D materials.

It is also a inexhaustible source of exciting mathematical and numerical problems of various nature: linear and nonlinear partial differential equations, optimization and control, stochastic processes and Monte Carlo methods, spectral theory, group theory, non-commutative algebra and geometry, statistical methods and machine learningâ€¦

In this talk, I will give an overview of some mathematical models and numerical methods used to predict macroscopic properties of a material from its atomic structure. I will first present the case of perfect crystals, where e.g. band structure diagrams constructed from Bloch-Floquet theory allow us to understand the difference in behavior between conductors, semiconductors, and insulators, as well as some of the properties of emerging topological materials. I will then discuss recent advances in the challenging field of modeling and simulating disordered systems such as crystals with defects, doped semiconductors, glasses, quasicrystals, or multilayer 2D materials.

Eric CancĂ¨s is a professor at Ecole des Ponts ParisTech and the head of the Applied Mathematics department. He is also affiliated to Inria Paris. He graduated from Ecole Polytechnique (engineering degree, 1992), Ecole des Ponts ParisTech (PhD, 1998) and University Paris Dauphine (habilitation, 2003). His research focuses on quantum and classical molecular simulation, in particular on Density Functional Theory, implicit solvent models for quantum chemistry and molecular biology, and electronic structure models for materials science. He is a member of the editorial boards of ESAIM: Mathematical Modeling and Numerical Analysis, SIAM Journal of Scientific Computing, Multiscale Modeling and Simulation (SIAM MMS), and Journal of Computational Mathematics. He was awarded the Blaise Pascal Prize in 2009, and the Dargelos Prize in 2017. He was an invited lecturer at the International Congress of Mathematicians in 2014. He is one of the four PIs of the European Research Council (ERC) Synergy grant EMC2 (Extreme-scale Mathematically-based Computational Chemistry).