Singularities in Discrete Systems

Abstract

Discrete systems are ubiquitous in applications. Their analysis and simulation call for taming their inherent multiscale character, as microscopic dynamics lead to the emergence of structures across scales. This workshop brought together leading experts in the calculus of variations, discrete systems, and materials science to explore cutting-edge topics at the intersection of mathematics and physical modelling. Presentations spanned a variety of themes, including dislocation dynamics, crystallization, micromagnetics, fracture mechanics, and discrete-to-continuum transitions. Particular emphasis was placed on the rigorous analysis of singular structures, nonlocal interactions, and energy-driven pattern formation. Several talks also underscored emerging connections with data science.