Explore the intricacies of Bose-Einstein condensate thermal fluctuations in this comprehensive lecture by Prof. Kazimierz Rzążewski from the Center for Theoretical Physics PAS. Delve into the historical context, starting with Schrödinger's observations on statistical ensemble choices, and trace the evolution of this hot topic through asymptotic results and partition function recurrence relations. Examine the controversial role of weak collisions and recent experimental measurements by Jan Arlt's group in Aarhus. Learn about the novel Fock States Sampling method, which enables computation of non-zero temperature properties for both canonical and microcanonical statistics in Bose gases with up to 100,000 particles. Investigate the method's application to weakly interacting gases trapped in boxes, including revisited results on interaction-induced shifts in critical temperature. Cover topics such as temperature, canonical ensemble, aspect ratio, experimental results, collisions, Metropolis dynamics, microeconomic calculations, Bogaluru approximation, maximum fluctuations, and combined results in this in-depth exploration of Bose-Einstein condensate physics. Read more