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Explore a comprehensive lecture on geometric phases for quasi-free fermions at finite temperature, presented by Andrés Fernando Reyes Lega at the Dublin Institute for Advanced Studies. Delve into the discussion of a Z_2 index associated with quadratic gapped Hamiltonians describing fermionic systems in the context of self-dual CAR C*-algebras. Examine concrete examples illustrating the physical relevance of this invariant. Investigate preliminary results on extending this invariant to the finite temperature case, based on a generalization of the geometric phase to mixed states. Gain insights into advanced concepts in quantum physics and mathematical physics over the course of this 1 hour and 36 minute presentation.
