TITLE: Classical and quantum many-body correlations SPEAKER: Stephan Weis (Independent Researcher, formerly Max-Planck-Institute for Mathematics) ABSTRACT: This talk begins with definitions of low-order correlations in probability distributions induced by classes of subsystems: Monomial maps, toric varieties, factorization, Hierarchical models (Lauritzen 1996, Geiger et al. 2006, Kahle 2010). Examples are discussed. Hierarchical models are defined for probability distributions and for quantum systems using the maximum-entropy principle. In a unified classical-quantum view we explain the idea of irreducible correlation (Linden et al. 2002, Zhou 2008) and its representation as the divergence from a the set of thermal states of local Hamiltonians (Amari 2001, Ay et al. 2011). We point out differences between the classical and quantum setting (continuity, local maximizers). This is joint work with Andreas Knauf (Erlangen), Nihat Ay (Leipzig, Santa Fe), Ming-Jing Zhao (Beijing)