"From affine geometry to statistical structures", a meeting in honour of prof. Barbara Opozda

7-8 June 2024

Faculty of Mathematics and Computer Science Jagiellonian University in Krakow

ul. Prof. S. Łojasiewicza 6, 30-348 Kraków

Scientific Committee:

prof. dr hab. Barbara Opozda (Uniwersytet Jagielloński)

prof. Michel Nguiffo Boyom (Université de Montpellier)

Organizing Committee:

Aleksandra Borówka, Paweł Raźny

List of invited speakers:

Vicente Cortés (Hamburg) Homogeneous cones associated with Clifford modules

Ryszard Deszcz (Wrocław)

Eduardo Garcia Rio (Santiago de Compostela ) Conformally Einstein metrics on Lorentzian Lie groups

Abstract: A pseudo-Riemannian manifold $(M,g)$ is said to be \emph{conformally Eisntein} if there is an Einstein representative of the conformal class $[g]$. Although the necessary and sufficient conditions for a metric to be conformally Einstein were obtained by Brinkmann at the beginning of last century, such conditions are encoded in a overdetermined PDE whose analysis is surprisingly

difficult, and only a very few classification results are available. Dimension four is the first non-trivial case for analysis and our purpose is to present the classification of such metrics within the family of left-invariant Lorentz metrics on four-dimensional Lie groups. As a by side consequence we obtain a full description of all Bach-flat Lorentzian Lie groups, which is of independent interest in conformal gravity.

Janusz Grabowski (Warszawa) Information Geometry on groupoids

Michel Nguiffo Boyom (Montpellier) Degeneracy of Koszul Pointed Homological Series of Lie Algebroids.
Abstract: In 1972 Jean-Louis Koszul introduced the homology of complex of differential forms of high order. He pointed out a few examples of high order cohomology classes which never vanish. The framework of this talk is made up of the category of Lie algebroids and the category of modules of Lie algebroids. The topic of discussions is the cohomology of Lie algebroids with values in their modules. A construction initiated by Koszul is extended in these frames. We point out certain homological vanishing theorems which present a great interest in both the Cartan Geometry and the Differential Geometry.

Zoran Rakic (Belgrade) Оn the Schwarzschild type metric in the nonlocal de Sitter $\sqrt{dS}$ gravity

Aleksy Tralle (Olsztyn)

Pol Verstraelen (Leuven) On the natural beauty of Riemannian spaces (virtual attendance)

Regular speakers:

1. Rouzbeh Mohseni (Warszawa)

2. Piotr Kopacz (Gdynia) Matsumoto’s problem in Riemann-Finsler geometry – generalization and extension

Abstract: By introducing the concept of a slippery slope we generalize and interlink the Matsumoto slope-of-a-mountain problem with the Zermelo navigation problem on Riemannian manifolds under the influence of a gravitational wind. The purely geometric solutions for time geodesics in the slippery slope model are discussed by means of Finsler geometry.

On Friday lectures will be in the lecture number 1094 and on Saturday in 1016

This meeting is funded by ID.UJ and by the grant Constructions of hiperkähler and quaternion-Kähler manifolds 2022/47/D/ST1/02197