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Explore fundamental concepts of Statistical Mechanics in this graduate-level lecture from IMPA's 2025 Summer School, delivered in Portuguese by Professor Hubert Lacoin. Delve into essential topics including Hamiltonian systems, Liouville's theorem, Poincaré recurrence theorem, Birkhoff's theorem, Boltzmann hypothesis, statistical ensembles, Gibbs measure, Ising model, thermodynamic limit, FKG inequality, phase transitions, phase diagrams, FK models, and Pirogov-Sinai theory. Drawing from renowned references like Feynman's Statistical Mechanics lectures, Presutti's work on scaling limits, and specialized texts by Friedli and Velenik, master advanced statistical mechanics concepts through comprehensive theoretical discussions. This master's level course serves as the first session in a series, with additional requirements available for doctoral students.
