Research

Our current research interests include:

• Applied and Computational Geometry
• Interdisciplinary Mathematical Modeling
• Quantitative Biology
• Medical Imaging
• Metamaterial Design
• Geometry Processing
• Scientific Computing
• Geometric Machine Learning

1. Computational geometry and visualization

Spherical conformal parameterization

• (For genus-0 surface meshes) P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), 67-94, 2015.
• (For genus-0 point clouds) G. P.-T. Choi, K. T. Ho, and L. M. Lui, Spherical conformal parameterization of genus-0 point clouds for meshing. SIAM Journal on Imaging Sciences, 9(4), 1582-1618, 2016.
• (For genus-0 surface meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.

Disk conformal parameterization

• (For simply-connected open surface meshes) P. T. Choi and L. M. Lui, Fast disk conformal parameterization of simply-connected open surfaces. Journal of Scientific Computing, 65(3), 1065-1090, 2015.
• (For simply-connected open surface meshes) G. P. T. Choi and L. M. Lui, A linear formulation for disk conformal parameterization of simply-connected open surfaces. Advances in Computational Mathematics, 44(1), 87-114, 2018.
• (For simply-connected open surface meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.

Rectangular conformal parameterization

• (For simply-connected open surface meshes and point clouds) T. W. Meng, G. P. T. Choi, and L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.

Conformal parameterization onto a non-convex domain

• (For simply-connected open surface meshes) G. P. T. Choi, Y. Chen, L. M. Lui, and B. Chiu, Conformal mapping of carotid vessel wall and plaque thickness measured from 3D ultrasound images. Medical & Biological Engineering & Computing, 55(12), 2183-2195, 2017.

Free-boundary conformal parameterization

• (For simply-connected open surface meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.
• (For simply-connected open point clouds) G. P. T. Choi, Y. Liu, and L. M. Lui, Free-boundary conformal parameterization of point clouds. Journal of Scientific Computing, 90(1), 14, 2022.

Conformal and quasi-conformal parameterization of multiply-connected surfaces

• (For multiply-connected surface meshes) G. P. T. Choi, Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory. Journal of Scientific Computing, 87(3), 70, 2021.
• (For multiply-connected surface meshes) Z. Zhu, G. P. T. Choi, and L. M. Lui, Parallelizable global quasi-conformal parameterization of multiply connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 15(4), 1765-1807, 2022.
• (For multiply-connected surface meshes) S. Yao and G. P. T. Choi, Conformal tubular parameterization and toroidal bending of tube-like surfaces. Preprint, arXiv:2605.16305, 2026.

Spherical quasi-conformal parameterization

• (For genus-0 surface meshes) G. P. T. Choi, M. H. Y. Man, and L. M. Lui, Fast spherical quasiconformal parameterization of genus-0 closed surfaces with application to adaptive remeshing. Geometry, Imaging and Computing, 3(1-2), 1-29, 2016.

Spherical landmark aligned optimized conformal parameterization

• (For genus-0 surface meshes) P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), 67-94, 2015.

Disk landmark-based quasi-conformal parameterization

• (For simply-connected open surface meshes) Y. Guo, Q. Chen, G. P. T. Choi, and L. M. Lui, Automatic landmark detection and registration of brain cortical surfaces via quasi-conformal geometry and convolutional neural networks. Computers in Biology and Medicine, 163, 107185, 2023.

Ellipsoidal conformal and quasi-conformal parameterization

• (For genus-0 surface meshes) G. P. T. Choi, Fast ellipsoidal conformal and quasi-conformal parameterization for genus-0 closed surfaces. Journal of Computational and Applied Mathematics, 447, 115888, 2024.

Teichmüller extremal map

• (For simply-connected open point clouds) T. W. Meng, G. P. T. Choi, and L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.
• (For simply-connected open surface meshes) G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A, 474(2217), 20170905, 2018.

General quasi-conformal mapping frameworks and analyses

• (For volumetric domains) D. Zhang, G. P. T. Choi, J. Zhang, and L. M. Lui, A unifying framework for n-dimensional quasi-conformal mappings. SIAM Journal on Imaging Sciences, 15(2), 960-988, 2022.
• G. P. T. Choi and L. M. Lui, Recent developments of surface parameterization methods using quasi-conformal geometry. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, Springer, Cham, 1483-1523, 2023.
• Z. Lyu and G. P. T. Choi, Beltrami coefficient and angular distortion of discrete geometric mappings. Preprint, arXiv:2603.19240.

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

• (For simply-connected open surface meshes) G. P. T. Choi and C. H. Rycroft, Density-equalizing maps for simply connected open surfaces. SIAM Journal on Imaging Sciences, 11(2), 1134-1178, 2018.
• (For simply-connected open surface meshes) G. P. T. Choi, B. Chiu, and C. H. Rycroft, Area-preserving mapping of 3D ultrasound carotid artery images using density-equalizing reference map. IEEE Transactions on Biomedical Engineering, 67(9), 1507-1517, 2020.
• (For simply-connected open surface meshes) M. Shaqfa, G. P. T. Choi, G. Anciaux, and K. Beyer, Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. Journal of Computational Physics, 522, 113578, 2025.
• (For simply-connected open surface meshes) G. P. T. Choi and M. Shaqfa, Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces. Journal of Computational and Applied Mathematics, 461, 116455, 2025.
• (For multiply-connected open surface meshes) Z. Lyu, G. P. T. Choi, and L. M. Lui, Bijective density-equalizing quasiconformal map for multiply connected open surfaces. SIAM Journal on Imaging Sciences, 17(1), 706-755, 2024.
• (For genus-0 surface meshes) Z. Lyu, L. M. Lui, and G. P. T. Choi, Spherical density-equalizing map for genus-0 closed surfaces. SIAM Journal on Imaging Sciences, 17(4), 2110-2141, 2024.
• (For genus-0 surface meshes) Z. Lyu, L. M. Lui, and G. P. T. Choi, Ellipsoidal density-equalizing map for genus-0 closed surfaces. Advances in Computational Mathematics, 52, 30, 2026.
• (For genus-1 surface meshes) S. Yao and G. P. T. Choi, Toroidal density-equalizing map for genus-one surfaces. Journal of Computational and Applied Mathematics, 472, 116844, 2026.
• (For volumetric domains) G. P. T. Choi and C. H. Rycroft, Volumetric density-equalizing reference map with applications. Journal of Scientific Computing, 86(3), 41, 2021.
• (For planar or volumetric domains) Y. Huang, L. M. Lui, and G. P. T. Choi, Learning-based density-equalizing map. AIMS Mathematics, 10(11), 25756-25790, 2025.
• (For planar or volumetric domains) Y. Huang, L. M. Lui, and G. P. T. Choi, Resolution-free neural surrogates for geometric parameterization and mapping with spatially varying fields. Preprint, arXiv:2605.28551.
• (For tetrahedral meshes) Z. Lyu, Q. Chen, G. P. T. Choi, and L. M. Lui, Volumetric parameterization for 3-dimensional simply-Connected manifolds. Preprint, arXiv:2506.17025.

Optimal mass transport map

• (For genus-0 surface meshes) A. Pumarola, J. Sanchez-Riera, G. P. T. Choi, A. Sanfeliu, and F. Moreno-Noguer, 3DPeople: Modeling the geometry of dressed humans. The IEEE International Conference on Computer Vision (ICCV), 2242-2251, 2019.
• (For simply-connected open/closed surface meshes) A. Giri*, G. P. T. Choi*, and L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. (*equal contribution)
• (For simply-connected open/closed surface meshes) G. P. T. Choi, A. Giri, and L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022.

Image triangulation and registration

• C. P. Yung, G. P. T. Choi, K. Chen, and L. M. Lui, Efficient feature-nased image registration by mapping sparsified features. Journal of Visual Communication and Image Representation, 55, 561-571, 2018.
• H. Law, G. P. T. Choi, K. C. Lam, and L. M. Lui, Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, 16(4), 1019-1046, 2022.
• D, Zhang, G. P. T. Choi, J. Zhang, and L. M. Lui, A unifying framework for n-dimensional quasi-conformal mappings. SIAM Journal on Imaging Sciences, 15(2), 960-988, 2022.

Surface harmonics

• A. Giri*, G. P. T. Choi*, and L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. (*equal contribution)
• G. P. T. Choi, A. Giri, and L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022.
• M. Shaqfa, G. P. T. Choi, and K. Beyer, Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches. Powder Technology, 393, 837-856, 2021.
• M. Shaqfa, G. P. T. Choi, G. Anciaux, and K. Beyer, Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. Journal of Computational Physics, 522, 113578, 2025.
• G. P. T. Choi and M. Shaqfa, Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces. Journal of Computational and Applied Mathematics, 461, 116455, 2025.

Mappings for astronomy

• B. Jarvis, G. P. T. Choi, B. Hockman, B. Morrell, S. Bandopadhyay, D. Lubey, J. Villa, S. Bhaskaran, D. Bayard, and I. A. Nesnas, 3D shape reconstruction of small bodies from sparse features. IEEE Robotics and Automation Letters, 6(4), 7089-7096, 2021.

Mappings for robotics

• G. Notomista, G. P. T. Choi, and M. Saveriano, Reactive robot navigation using quasi-conformal mappings and control barrier functions. IEEE Transactions on Control Systems Technology, 33(3), 928-939, 2025.

2. Mathematics of materials and structures

Kirigami metamaterials

• G. P. T. Choi, L. H. Dudte, and L. Mahadevan, Programming shape using kirigami tessellations. Nature Materials, 18, 999-1004, 2019.
• S. Chen*, G. P. T. Choi*, and L. Mahadevan, Deterministic and stochastic control of kirigami topology. Proceedings of the National Academy of Sciences, 117(9), 4511-4517, 2020. (*equal contribution)
• G. P. T. Choi, L. H. Dudte, and L. Mahadevan, Compact reconfigurable kirigami. Physical Review Research, 3(4), 043030, 2021.
• L. Liu*, G. P. T. Choi*, and L. Mahadevan, Wallpaper group kirigami. Proceedings of the Royal Society A, 477(2252), 20210161, 2021. (*equal contribution)
• L. Liu*, G. P. T. Choi*, and L. Mahadevan, Quasicrystal kirigami. Physical Review Research, 4(3), 033114, 2022. (*equal contribution)
• L. H. Dudte*, G. P. T. Choi*, K. P. Becker, and L. Mahadevan, An additive framework for kirigami design. Nature Computational Science, 3(5), 443-454, 2023. (*equal contribution)
• G. P. T. Choi, L. Liu, and L. Mahadevan, Explosive rigidity percolation in kirigami. Proceedings of the Royal Society A, 479(2271), 20220798, 2023.
• G. P. T. Choi, Computational design of art-inspired metamaterials. Nature Computational Science, 4(8), 549-552, 2024.
• Q. Jiang and G. P. T. Choi, PyKirigami: An interactive Python simulator for kirigami structures. Preprint, arXiv:2508.15753.
• H. H. C. Cheng and G. P. T. Choi, Monotile kirigami. Preprint, arXiv:2604.19586.

Origami metamaterials

• L. H. Dudte, G. P. T. Choi, and L. Mahadevan, An additive algorithm for origami design. Proceedings of the National Academy of Sciences, 118(21), e2019241118, 2021.
• G. P. T. Choi, Computational design of art-inspired metamaterials. Nature Computational Science, 4(8), 549-552, 2024.
• R. Li and G. P. T. Choi, Explosive rigidity percolation in origami. Proceedings of the Royal Society A, 481(2316), 20240826, 2025.
• R. Li and G. P. T. Choi, Rigidity control of general origami structures. Communications Physics, 9, 217, 2026.
• K. H. Lai, H. T. Tsang, G. P. T. Choi, and L. M. Lui, Optimization of constrained quasiconformal mapping for origami design. Preprint, arXiv:2604.20137.

Assemblies, networks, and other architected materials

• G. P. T. Choi, S. Chen, and L. Mahadevan, Control of connectivity and rigidity in prismatic assemblies. Proceedings of the Royal Society A, 476(2244), 20200485, 2020.
• S. Chen, F. Giardina, G. P. T. Choi, and L. Mahadevan, Modular representation and control of floppy networks. Proceedings of the Royal Society A, 478(2264), 20220082, 2022.
• T. Lau and G. P. T. Choi, Explosive connectivity and mechanical rigidity in cubic lattice structures. Preprint, arXiv:2511.01537.
• M. Y. L. Yip and G. P. T. Choi, Low-distortion planar embedding of rod-based structures. Preprint, arXiv:2602.07789.
• J. Fang, X. Ding, and G. P. T. Choi, Geometric quantification for nonlinear deformation in knitted fabrics. Preprint, arXiv:2604.19030.

3. Quantitative biology and physics

Brain morphometry and morphogenesis

• P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), 67-94, 2015.
• Y. Guo, Q. Chen, G. P. T. Choi, and L. M. Lui, Automatic landmark detection and registration of brain cortical surfaces via quasi-conformal geometry and convolutional neural networks. Computers in Biology and Medicine, 107185, 2023.
• G. P. T. Choi, C. Liu, S. Yin, G. Séjourné, R. S. Smith, C. A. Walsh, and L. Mahadevan, Biophysical basis for brain folding and misfolding patterns in ferrets and humans. eLife, 14, RP107141, 2025.
• S. Yin, C. Liu, G. P. T. Choi, Y. Jung, K. Heuer, R. Toro, and L. Mahadevan, Morphogenesis and morphometry of brain folding patterns across species. eLife, 14, RP107138, 2025.

Face shape analysis

• T. W. Meng, G. P. T. Choi, and L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.

Shape analysis of carotid artery

• G. P. T. Choi, Y. Chen, L. M. Lui, and B. Chiu, Conformal mapping of carotid vessel wall and plaque thickness measured from 3D ultrasound images. Medical & Biological Engineering & Computing, 55(12), 2183-2195, 2017.
• G. P. T. Choi, B. Chiu, and C. H. Rycroft, Area-preserving mapping of 3D carotid ultrasound images using density-equalizing reference map. IEEE Transactions on Biomedical Engineering, 67(9), 1507-1517, 2020.

Planar morphometry and morphogenesis

• G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A, 474(2217), 20170905, 2018.
• H. Li and G. P. T. Choi, Planar morphometry via functional shape data analysis and quasi-conformal mappings. Preprint, arXiv:2605.05778.

Tooth morphometry

• G. P. T. Choi, H. L. Chan, R. Yong, S. Ranjitkar, A. Brook, G. Townsend, K. Chen, and L. M. Lui, Tooth morphometry using quasi-conformal theory. Pattern Recognition, 99, 107064, 2020.
• G. P. T. Choi, D. Qiu, and L. M. Lui, Shape analysis via inconsistent surface registration. Proceedings of the Royal Society A, 476(2242), 20200147, 2020.

Avian skull and beak morphometry and morphogenesis

• S. Al-Mosleh, G. P. T. Choi, A. Abzhanov, and L. Mahadevan, Geometry and dynamics link form, function and evolution of finch beaks. Proceedings of the National Academy of Sciences, 118(46), e2105957118, 2021.
• S. Mosleh*, G. P. T. Choi*, G. M. Musser, H. F. James, A. Abzhanov, and L. Mahadevan, Beak morphometry and morphogenesis across avian radiations. Proceedings of the Royal Society B, 290(2007), 20230420, 2023. (*equal contribution)
• K. Lau and G. P. T. Choi, Robust parametric estimation of avian cranial morphology. Preprint, arXiv:2511.06426.
• K. Lau and G. P. T. Choi, PhyloSDF: Phylogenetically-conditioned neural generation of 3D skull morphology via residual flow matching. Preprint, arXiv:2604.25371.

Egg patterns

• T. Dixit, G. P. T. Choi*, S. Al-Mosleh*, J. Lund, J. Troscianko, C. Moya, L. Mahadevan, and C. N. Spottiswoode, Combined measures of mimetic fidelity explain imperfect mimicry in a brood parasite-host system. Biology Letters, 19(2), 20220538, 2023. (*equal contribution)

Flower morphology

• M. B. Edwards, G. P. T. Choi, N. Derieg, Y. Min, A. C. Diana, S. A. Hodges, L. Mahadevan, E. M. Kramer, and E. S. Ballerini, Genetic architecture of floral traits in bee- and hummingbird-pollinated sister species of Aquilegia (columbine). Evolution, 75(9), 2197-2216, 2021.

Quasi-conformal flows for morphodynamics

• S. Mosleh*, G. P. T. Choi*, and L. Mahadevan, Data-driven quasi-conformal morphodynamic flows. Proceedings of the Royal Society A, 481(2314), 20240527, 2025. (*equal contribution)

Physical modelling of natural phenomena

• A. Chakrabarti, G. P. T. Choi, and L. Mahadevan, Self-excited motions of volatile drops on swellable sheets. Physical Review Letters, 124(25), 258002, 2020.
• T. Ohmura, D. J. Skinner, K. Neuhaus, G. P. T. Choi, J. Dunkel, and K. Drescher, In vivo microrheology reveals local elastic and plastic responses inside three-dimensional bacterial biofilms. Advanced Materials, 36(29), 2314059, 2024.
• O. Y. L. Chau, R. Bendick, G. P. T. Choi, and L. Mahadevan, How geometry of subduction zones correlates with earthquake dynamics. Preprint, arXiv:2606.02520.

4. Geometry and learning

Learning-based shape modelling

• A. Pumarola, J. Sanchez-Riera, G. P. T. Choi, A. Sanfeliu, and F. Moreno-Noguer, 3DPeople: Modeling the geometry of dressed humans. The IEEE International Conference on Computer Vision (ICCV), 2242-2251, 2019.
• K. Lau and G. P. T. Choi, PhyloSDF: Phylogenetically-conditioned neural generation of 3D skull morphology via residual flow matching. Preprint, arXiv:2604.25371.

Learned-based geometric mappings

• H. Law, G. P. T. Choi, K. C. Lam, and L. M. Lui, Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, 16(4), 1019-1046, 2022.
• Y. Guo, Q. Chen, G. P. T. Choi, and L. M. Lui, Automatic landmark detection and registration of brain cortical surfaces via quasi-conformal geometry and convolutional neural networks. Computers in Biology and Medicine, 163, 107185, 2023.
• Y. Huang, L. M. Lui, and G. P. T. Choi, Learning-based density-equalizing map. AIMS Mathematics, 10(11), 25756-25790, 2025.
• Y. Huang, L. M. Lui, and G. P. T. Choi, Resolution-free neural surrogates for geometric parameterization and mapping with spatially varying fields. Preprint, arXiv:2605.28551.

Learning collective dynamics

• R. Supekar, B. Song, A. Hastewell, G. P. T. Choi, A. Mietke, and J. Dunkel, Learning hydrodynamic equations for active matter from particle simulations and experiments. Proceedings of the National Academy of Sciences, 120(7), e2206994120, 2023.

Geometric machine learning

• T. Lau and G. P. T. Choi, The normalized maximum likelihood for regular non-smooth models: Measure-theoretic foundations and geometric sampling. Preprint, arXiv:2605.24477.
• T. Lau and G. P. T. Choi, Exact Schur-Sylvester dimensionality reductions for non-smooth stochastic complexity and manifold sampling. Preprint, arXiv:2606.23867.
• G. P. T. Choi*, K. Dao Duc*, S. Faigenbaum-Golovin*, K. Habermann*, E. Hartman*, C. von Tycowicz*, C. Zhang*, W. Zhao*, and F. Zhou*, Learning the geometry of data: A mathematical review of shape space analysis. Preprint, arXiv:2606.17022. (*equal contribution)

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