W. E

Princeton University

**Mathematical Theory of Solids: From Atomic to Macroscopic
Scales**

Princeton University

How do we build a mathematical theory for the macroscopic deformation of solids starting from atomistic models? This talk will present a review of current work on this problem at zero temperature. It will cover the following topics: (1) Stability of crystals and the validity of Cauchy-Born rule for the elastic regime; (2) instability of crystals and mechanisms of defect formation; (3) generalized Peierls-Nabarro models for defect structure and dynamics.