Geometry, Mechanics and Control Seminar

Information Geometry on Lie Algebroids

Speaker:  Janusz Grabowski (Institute of Mathematics, Polish Academy of Sciences))
Date:  Friday, 18 March 2022 - 15:30
Online:   us06web.zoom.us/j/7555463367 (ID: 755 546 3367)

Abstract:

I will try to covince the audience  that the proper general setting for statistical and information geometry is the one provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to a two-form and a three-form on the corresponding Lie algebroid. If the two-form is non-degenerate, it defines a pseudo-Riemannian metric on the Lie algebroid and a family of Lie algebroid torsion-free connections, including the Levi-Civita connection of the metric. In this framework, the standard two-point contrast functions are understood as functions on the pair groupoid MxM and generate astandard (pseudo-)Riemannian metrics on M and families of affine connections on the Lie algebroid TM. Studying also infinite-dimensional examples, I will present a contrast function defining the Fubini-Study metric on the Hilbert projective space.
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