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作者：Castro, A.; Cordoba, D.; Faraco, D.
作者单位：Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidad Carlos III de Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); Complutense University of Madrid; Autonomous University of Madrid
摘要：We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H-5 initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed.
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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：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 ...
