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Shimpei Kobayashi

Differential Geometry and Integrable Systems

Surface theory, harmonic maps, loop groups, and geometric structures

I work on differential geometry and integrable systems, with emphasis on surface theory, harmonic maps, loop group methods, Teichmüller-type geometry, minimal Lagrangian geometry, and Jordan-theoretic structures in affine and statistical geometry.

Professor, Department of Mathematics, Hokkaido University

My research is centered on the idea that classical geometric structure equations often acquire a spectral parameter in special geometric problems and thereby become part of an integrable system. This viewpoint connects surface geometry, harmonic maps, loop groups, discrete differential geometry, Teichmüller theory, and affine/statistical geometry.

Research areas

  • Integrable systems and surface geometry
    Minimal, constant mean curvature, and constant Gaussian curvature surfaces; DPW and loop group methods.

  • Teichmüller theory and harmonic maps
    Complex landslides, harmonic maps, and geometric flows related to surface group geometry.

  • Minimal Lagrangian and product geometries
    Minimal Lagrangian surfaces in product spaces and complex quadrics.

  • Statistical, Hessian, and affine geometry
    Statistical manifolds, alpha-connections, Hessian structures, affine differential geometry, and Jordan-theoretic structures.

  • Discrete differential geometry
    Discrete CMC surfaces, discrete affine spheres, cross-ratio systems, and integrable discretizations.

Main sections

Book