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• Shock formation in solutions to the 2D compressible Euler equations in the presence of non-zero vorticity AI翻译
  作者：Luk, Jonathan; Speck, Jared
  作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
  摘要：We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple plane wave solutions, starting from smooth initial data, is stable under perturbations of the initial data that break the plane symmetry. Moreover, we provide a sharp asymptotic description of the singularity formation. The new feature of our work is that th...
• The structure of tame minimal dynamical systems for general groups AI翻译
  作者：Glasner, Eli
  作者单位：Tel Aviv University
  摘要：We use the structure theory of minimal dynamical systems to show that, for a general group Gamma, a tame, metric, minimal dynamical system (X, Gamma) has the following structure: [GRAPHICS] Here (i) (X) over tilde is a metric minimal and tame system (ii) eta is a strongly proximal extension, (iii) Y is a strongly proximal system, (iv) pi is a point distal and RIM extension with unique section, (v)theta, theta* and tau are almost one-to-one extensions, and (vi) sigma is an isometric extension. ...
• Types and unitary representations of reductive p-adic groups AI翻译
  作者：Ciubotaru, Dan
  作者单位：University of Oxford
  摘要：We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. Moreover, we show that every irreducible smooth G-representation contains a rigid type. This is a generalization of the unitarity criterion of Barbasch and Moy for representations wi...
• Potentially crystalline deformation rings and Serre weight conjectures: shapes and shadows AI翻译
  作者：Le, Daniel; Le Hung, Bao V.; Levin, Brandon; Morra, Stefano
  作者单位：University of Toronto; Institute for Advanced Study - USA; University of Arizona; Universite de Montpellier
  摘要：We prove the weight part of Serre's conjecture in generic situations for forms of U(3) which are compact at infinity and split at places dividing p as conjectured by Herzig (Duke Math J 149(1):37-116, 2009). We also prove automorphy lifting theorems in dimension three. The key input is an explicit description of tamely potentially crystalline deformation rings with Hodge-Tate weights (2, 1, 0) for unramified combined with patching techniques. Our results show that the (geometric) Breuil-M,zard...
• A projective variety with discrete, non-finitely generated automorphism group AI翻译
  作者：Lesieutre, John
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
  摘要：We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.
• Exponential decay of correlations for finite horizon Sinai billiard flows AI翻译
  作者：Baladi, Viviane; Demers, Mark F.; Liverani, Carlangelo
  作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Fairfield University; University of Rome Tor Vergata
  摘要：We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L-t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.
• On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad AI翻译
  作者：Beuzart-Plessis, Raphael
  作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over p-adic fields and we apply this formula to verify two consequences of a conjecture of Dipendra Prasad. One concerns the exact computation of the multiplicity of the Steinberg representation and the other the invariance of multiplicities by transfer among inner forms.
• Orbit spaces of unimodular rows over smooth real affine algebras AI翻译
  作者：Das, Mrinal Kanti; Tikader, Soumi; Zinna, Md. Ali
  作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; National Institute of Science Education & Research (NISER)
• A decomposition theorem for singular spaces with trivial canonical class of dimension at most five AI翻译
  作者：Druel, Stephane
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover, ,tale in codimension one, that decomposes as a product of an Abelian variety, and singular analogues of irreducible Calabi-Yau and irreducible holomorphic symplectic varieties.
• Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞ kernels AI翻译
  作者：Jabin, Pierre-Emmanuel; Wang, Zhenfu
  作者单位：University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; University of Pennsylvania
  摘要：We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space W--1,W-infinity thus including the Biot-Savart law and the point ...