Colloquium Abstracts

Date/Time/Location: Tuesday Oct 10, 2017 from 3:00-3:50pm in BAC 219

Speaker/Affiliation: Arnd Scheel, University of Minnesota

Title: Moduli Spaces of Growth Patterns

Abstract:

Interfaces or boundaries affect the formation of crystalline phases in sometimes quite dramatic ways. Examples range from the alignment of convection roles in Benard convection perpendicular to the boundary, to the robust patterning through presomites in limb formation. Mathematically, the object of interest is a moduli space of solutions to elliptic equations in unbounded domains. This moduli space contains the relation between rate of growth and crystallographic parameters such as the width and orientation of convection rolls or presomites. I will explain the role of this moduli space and give results and conjectures on its shape in examples, starting with simple convection-diffusion and phase separation problems, and concluding with Turing patterns.