Tomasz Miller (Copernicus Center, Jagiellonian University, Cracow)
In the late 19th century, Georg Cantor made a stunning discovery: in mathematics there is not just a single infinity, but an infinite hierarchy of "transfinite numbers." In my talk, I will briefly recall how this "Cantor’s paradise" (as Hilbert called it) is constructed. I will then turn to a more recent attempt to tame infinity, initiated by John H. Conway, who went on to discover an even richer - in a sense "ultimate" - number system: the surreal numbers. This system contains not only Cantor’s transfinites but also their reciprocals, the infinitesimals. I will close by reflecting on a natural question: why study such abstract objects at all?
Andrzej Zdziarski (CAMK, PAN, Warsaw)
In recent years, spins of merging black holes have been measured with relatively high accuracy from their gravitational-wave signals. They are generally low, with the estimated average effective spin parameter close to null. On the other hand, spins of many accreting black-hole binaries have been measured to be high, some close to the maximum spin parameter of 1, e.g., greater than 0.9985 at 3 sigma in Cygnus X-1. I will present our recent results regarding this discrepancy. In particular, I will discuss possible systematic effects affecting spin measurements in accreting systems and whether they can be reconciled with those from gravitational-wave observations. See New Astronomy Reviews (2026), 102, 101746 (arXiv:2506.00623).
Arpita Misra (Jagiellonian University, Cracow)
Daniela Turis-Gallo (Universidad de Valparaiso, Chile)
Dominika Król (Harvard Smithonian CfA)
Maciek Wielgus (Instituto de Astrofísica de Andalucía, IAA-CSIC, Granada, Hiszpania)
Laetitia Gibaud (Department of Physics, University of Białystok)
