WP1: Deformation quantization for statistical manifolds

Leader: Pierre Bieliavsky, UCL

WP1 is the study of the geometry of statistical manifolds associated to measured spaces carrying the measurable action of a group. Using techniques coming from statistical manifolds and, more generally, Information Geometry, WP1 aims at quantitatively studying the relations between three closely related but different fields: 

• Souriau’s Lie groups thermodynamics, 

• Koszul’s and Vinberg’s works on Hessian geometry for homogeneous complex bounded domains and analysis on regular cones, 

• Deformation Quantization and Harmonic Analysis on Lie groups and homogeneous spaces.