In-surface geometric analysis of hyperbolic structure formation in molecular simulations

Recent mathematical developments have paved the way for a new computational pipeline, which enables visualization and investigation of curved surfaces embedded in ordinary three-dimensional Euclidean space via their in-surface geometry, symmetry, and topology.

Notable examples of the emergence of these surfaces and their decorations include scaffolds in butterfly wing scales, membrane protein crystallization in cubic lipid phases, and elaborate block-copolymer structures.

This project will establish said pipeline, which will open a string of possibilities for new excursions in condensed matter physics, most notably to analyze self-assembled structures and defect patterns on curved surfaces from e.g. molecular simulations. Ideally, the project encompasses the development of novel simulation methodology based on the outcomes from the outlined approach as well.