Evolving crystal surfaces offer a prototypical case of mathematical modeling across the scales. In this talk I describe progress towards the
derivation and analysis of the related continuum laws. Microscopic laws are formulated for nanoscale objects, ``steps'', which compose crystal surfaces. Corresponding macroscopic laws and thermodynamic quantities are then derived from step models. Particular solutions of continuum equations are invoked to plausibly unify
experimental observations of decaying profiles. Free-boundary problems are studied for the evolution of crystal shapes with flat regions (``facets''), where boundary conditions are nonlocal with time. The formation of step bunches is studied via instabilities of appropriate partial differential equations for step positions.
Copyright. All Rights Reserved.