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math.DG2026
On Duality, Legendre Bundles and Deformations
N. C. Combe, P. G. Combe, H. K. Nencka
We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in informa…
math.DG2025
Exploring information geometry: Recent Advances and Connections to Topological Field Theory
Noémie C. Combe, Philippe G. Combe, Hanna K. Nencka
This introductory text arises from a lecture given in Göteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically incl…