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Explore recent mathematical developments in the analysis of Bose gases at positive temperature through this 38-minute conference lecture from the Erwin Schrödinger International Institute for Mathematics and Physics. Discover trace norm approximations for interacting Gibbs states of weakly interacting Bose gases and learn about computations of key physical quantities including particle distribution in condensates, joint distribution across momentum modes, and full counting statistics for particle subsets on the torus. Examine how these results utilize Gibbs state analysis as fundamental input and understand their expression through Bogoliubov versions of Gaussian free fields. Gain insights into new upper bounds for free energy in dilute Bose gases within the thermodynamic limit, based on collaborative research with leading experts in mathematical physics including Phan Tanh Nam, Marcin Napiorkowski, Blazej Ruba, Giulia Basti, Chiara Boccato, and Serena Cenatiempo.
