Title：LIE GROUPOIDS IN INFORMATION GEOMETRY
Reporter：Janusz Grabowski
Work Unit：Polish Academy of Sciences
Time：2023/05/10 15:50-17: 50
Address：ZOOM Id：904 645 6677，Password：2023
Summary of the report: After a general introduction to the information geometry, I will show that a natural 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 a standard (pseudo-)Riemannian metrics on M, and families of affine connections on the Lie algebroid TM.
Introduction of the Reporter: Professor Janusz Grabowski is the Head of the Department of Mathematical Physics and Differential Geometry in the Institute of Mathematics, Polish Academy of Sciences. His main interests are differential geometry and mathematical physics. As an author of about 140 scientific papers, he published fundamental results on Lie algebras of vector fields, diffeomorhism groups, Lie systems, Poisson and Jacobi manifolds, Lie groupoids and algebroids, Lagrangian and Hamiltonian mechanics (including mechanics on contact manifolds), supergeometry, geometry of quantum states and entanglement, etc. His personal page is https://www.impan.pl/~jagrab/.
