Geometry, handedness & frustration

The group develops the theory of geometrically frustrated soft matter, where the local interactions that material elements prefer cannot be simultaneously satisfied across the whole body. When a tissue, gel, or molecular assembly wants to adopt a rest geometry that does not fit into ordinary Euclidean space, the resulting residual stress reshapes the object: thin sheets buckle, ripple, or curl, and slender filaments writhe into helices. We formulate this using non-Euclidean elasticity, treating a body's intrinsic geometry as a reference metric and asking how it accommodates incompatibility through shape, energy, and selection between competing configurations.

A central theme is handedness, the breaking of mirror symmetry, and how molecular chirality propagates upward into the form and mechanics of larger structures. The group studies how chiral preferences accumulate, compete with frustration, and sometimes cancel, producing twisted ribbons, structural color, and emergent achirality from chiral constituents. These questions connect mathematical geometry to concrete systems in biology and materials, clarifying which observed shapes are mechanically inevitable and which reflect genuine design, and offering a vocabulary for understanding self-shaping matter.