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作者：Lewin, Mathieu; Nam, Phan Thanh; Rougerie, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; University of Munich; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP)
摘要：We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic quantum system converges to the Gibbs measure of a nonlinear Schrodinger-type classical field theory, in terms of partition functions and reduced density matrices. The Gibbs measure thus describes the behavior of the infinite Bose gas at criticality, that i...
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作者：Bjorklund, Michael; Kosloff, Zemer; Vaes, Stefaan
作者单位：Chalmers University of Technology; Hebrew University of Jerusalem; KU Leuven
摘要：We determine the Krieger type of nonsingular Bernoulli actions G curved right arrow Pi(g is an element of G)({0,1},mu(g)). When G is abelian, we do this for arbitrary marginal measures mu(g). We prove in particular that the action is never of type II infinity if G is abelian and not locally finite, answering Krengel's question for G=Z. When G is locally finite, we prove that type II infinity does arise. For arbitrary countable groups, we assume that the marginal measures stay away from 0 and 1...
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作者：Paolini, Giovanni; Salvetti, Mario
作者单位：University of Fribourg; California Institute of Technology; University of Pisa
摘要：We prove the K(pi,1) conjecture for affine Artin groups: the complexified complement of an affine reflection arrangement is a classifying space. This is a long-standing problem, due to Arnol'd, Pham, and Thom. Our proof is based on recent advancements in the theory of dual Coxeter and Artin groups, as well as on several new results and constructions. In particular: we show that all affine noncrossing partition posets are EL-shellable; we use these posets to construct finite classifying spaces ...
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作者：Chen, Dawei; Moeller, Martin; Sauvaget, Adrien; Zagier, Don
作者单位：Boston College; Goethe University Frankfurt; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite
摘要：A Correction to this paper has been published: https://doi.org/10.1007/s00222-020-00969-4
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作者：Neeman, Amnon
作者单位：Australian National University
摘要：In a 2006 article Schlichting conjectured that the negative K-theory of any abelian category must vanish. This conjecture was generalized in a 2019 article by Antieau, Gepner and Heller, who hypothesized that the negative K-theory of any category with a bounded t-structure must vanish. Both conjectures will be shown to be false.
