Statistical, Hessian, and Affine Geometry

This theme studies affine and statistical geometric structures, including alpha-connections, Hessian geometry, and geometric aspects of optimization.

Topics

• Statistical manifolds of normal and multivariate normal distributions.
• Alpha-connections and constant curvature statistical manifolds.
• Hessian geometry and convex optimization.
• Affine differential geometry and symmetric cones.
• Projectively flat affine connections and parallel cubic forms.

Representative publications

• A characterization of the alpha-connections on the statistical manifold of normal distributions.
• On a constant curvature statistical manifold.
• Geodesics of multivariate normal distributions and a Toda lattice type Lax pair.
• A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions.