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作者：Melvin, Paul; Schwartz, Hannah
作者单位：Bryn Mawr College; Princeton University
摘要：It is shown that any finite list of smooth closed simply-connected 4-manifolds homeomorphic to a given oneXcan be obtained by removing a single compact contractible submanifold (orcork) fromX, and then regluing it by powers of a boundary diffeomorphism. We then use this result to 'separate' finite families of corks embedded in a fixed 4-manifold.
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作者：Todorcevic, Stevo; Vidnyanszky, Zoltan
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; University of Toronto; California Institute of Technology
摘要：We show that there is no simple (e.g. finite or countable) basis for Borel graphs with infinite Borel chromatic number. In fact, it is proved that the closed subgraphs of the shift graph on [N](N) with finite (or, equivalently, <= 3) Borel chromatic number form a Sigma(1)(2)-complete set. This answers a question of Kechris and Marks and strengthens several earlier results.
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作者：Benedikter, Niels; Nam, Phan Thanh; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert
作者单位：University of Milan; University of Munich; International School for Advanced Studies (SISSA); University of Zurich; Institute of Science & Technology - Austria
摘要：We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a ne...
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作者：Beuzart-Plessis, Raphael
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We establish an explicit Plancherel decomposition for GL(n)(F)\GL(n)(E) where E/F is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai gamma-factors. We also give two applications of this Plancherel formula: first to the global Ichino-Ikeda conjecture for unitary groups by completing a comparison between local relative characters that was left open by Zhang (J Am Math Soc 27:541-612, 2014) and secondly to the Hiraga-Ichino-Ikeda ...
