Research


My current research interests include:



1. Mathematics of materials


Kirigami metamaterials

Origami metamaterials

Structural assemblies

Floppy networks

Droplets



2. Quantitative biology


Brain morphometry using landmark-matching quasi-conformal maps

Shape analysis of human facial point clouds using Teichmüller maps

Shape analysis of carotid artery using conformal/area-preserving maps

Insect wing morphometry using Teichmüller maps

Tooth morphometry using quasi-conformal theory

Morphometrics and morphogenesis of bird beaks

Egg patterns

Flower morphology

Collective dynamics



3. Computational geometry and visualization


Spherical conformal parameterization

Disk conformal parameterization

Rectangular conformal parameterization

Conformal parameterization onto a non-convex domain

Free-boundary conformal parameterization

Conformal and quasi-conformal parameterization of multiply-connected surfaces

Spherical quasi-conformal parameterization

Spherical landmark aligned optimized conformal parameterization

Disk landmark-based quasi-conformal parameterization

Teichmüller extremal map

Higher-dimensional quasi-conformal map

Density-equalizing map (area-preserving/with controllable area distortion)

Optimal mass transport map

Image triangulation and registration

Mappings and deep learning

Surface harmonics

Mappings for astronomy



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