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Explore a 35-minute conference talk by Frédéric Campana from the University of Nancy, presented at the University of Miami as part of the "Periods, Shafarevich Maps and Applications" conference. Delve into the study of nilpotent quotients of quasi-Kähler groups, focusing on smooth complex quasi-projective manifolds with proper quasi-Albanese maps. Discover how the torsionfree nilpotent quotients of the fundamental group of such manifolds relate to those of the Stein factorization of their quasi-Albanese image. Learn about the holomorphic convexity of the étale Galois cover associated with the nilpotent completion of the fundamental group. Examine the implications for 'special' manifolds and understand the limitations of these properties when the quasi-Albanese map is not proper. Gain insights into this collaborative work with R. Aguilar, which builds upon and complements previous research in the field.