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Special Issue: Affine differential geometry and Hesse geometry - a tribute and memorial to Jean–Louis Koszul

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Jean–Louis Koszul (3 Jan 1921–12 Jan 2018) was a French mathematician with prominent influence on a wide range of mathematical fields. He was a second-generation member of Bourbaki, with several notions in geometry and algebra named after him, such as Koszul connection, Koszul complex, Koszul cohomology, Koszul duality, and so on. He made a great contribution to the fundamental theory of differential geometry, especially the theory of linear (Koszul) connections and affinely flat manifolds, providing foundation of information geometry. This special issue is dedicated to Koszul for the mathematics he developed that bear well on information sciences.

The special issue contains six papers. They cover a wide range of topics such as affine differential geometry over statistical manifolds, Hesse geometry with Fisher information metric, Lie group representations, pre-Lie algebras and their cohomology, geometric mechanics and thermodynamics, and statistical models over homogeneous spaces. These subjects are related to each other, and have intrinsic relations to Koszul’s mathematics.

This special issue should be also a spot of such encounters of various researchers, from which further collaborations will arise in the future.

Editors

  • Hideyuki Ishi Hideyuki Ishi

    Hideyuki Ishi

    Professor, Graduate School of Science, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka, 558-8585, Japan

Articles (7 in this collection)