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Gamma-positivity provides a powerful method to prove
    unimodality for polynomials with real symmetric coefficients. It
    appeared in the seventies, in work of Foata and Sch"utzenberger
    on the Eulerian polynomials, and attracted considerable attention
    after work of Br"ande'n on poset Eulerian polynomials and Gal on
    triangulations of spheres. Gamma-positivity admits a natural
    equivariant generalization. This lecture will discuss some of
    few known instances of equivariant gamma-positivity, related to
    colored permutations and derangements on the enumerative side,
    and to barycentric and edgewise subdivisions on the geometric
    side. Somewhat surprisingly, the proofs involve group actions
    on the homology of posets.