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作者：Bader, Uri; Furman, Alex; Sauer, Roman
作者单位：Technion Israel Institute of Technology; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Chicago
摘要：We study rigidity properties of lattices in , na parts per thousand yen3, and of surface groups in in the context of integrable measure equivalence. The results for lattices in , na parts per thousand yen3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n=2 we show that cocompact lattices in allow a similar integrable measure equivalence classification.
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor
作者单位：CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Princeton University
摘要：We consider the energy critical Schrodinger map problem with the 2-sphere target for equivariant initial data of homotopy index k=1. We show the existence of a codimension one set of smooth well localized initial data arbitrarily close to the ground state harmonic map in the energy critical norm, which generates finite time blowup solutions. We give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy.
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作者：Lackenby, Marc; Meyerhoff, Robert
作者单位：University of Oxford; Boston College
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作者：De Lellis, Camillo; Szekelyhidi, Laszlo, Jr.
作者单位：University of Zurich; Leipzig University
摘要：We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.
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作者：Masmoudi, Nader
作者单位：New York University
摘要：Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties. The proof uses many weak convergence techniques. In particular it is based on the control ...
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作者：Bhargava, Manjul; Shankar, Arul; Tsimerman, Jacob
作者单位：Princeton University; Institute for Advanced Study - USA; Harvard University
摘要：We give simple proofs of the Davenport-Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the number of 3-torsion elements in the class groups of quadratic fields having bounded discriminant. We also establish second main terms for these theorems, thus proving a conjecture of Roberts. Our arguments provide natural interpretations for the various constants appearing in these theorems in terms of local masses of ...
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作者：Kim, Sung-Yeon; Zaitsev, Dmitri
作者单位：Kangwon National University; Trinity College Dublin
摘要：Our goal is to establish what seems to be the first rigidity result for CR embeddings between Shilov boundaries of bounded symmetric domains of higher rank. The result states that any such CR embedding is the standard linear embedding up to CR automorphisms. Our basic assumption extends precisely the well-known optimal bound for the rank one case. There are no other restrictions on the ranks, in particular, the difficult case when the target rank is larger than the source rank is also allowed.
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作者：Yalkinoglu, Bora
作者单位：Max Planck Society
摘要：This paper has two parts. In the first part we construct arithmetic models of Bost-Connes systems for arbitrary number fields, which has been an open problem since the seminal work of Bost and Connes (Sel. Math. 1(3): 411-457, 1995). In particular our construction shows how the class field theory of an arbitrary number field can be realized through the dynamics of a certain operator algebra. This is achieved by working in the framework of Endomotives, introduced by Connes, Consani and Marcolli...
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作者：Brown, Francis C. S.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Let k be a totally real number field. For every odd na parts per thousand yen3, we construct an element in the category MT(k) of mixed Tate motives over k out of the quotient of a product of hyperbolic spaces by an arithmetic group. By a volume calculation, we prove that its period is a rational multiple of , where denotes the special value of the Dedekind zeta function of k. We deduce that the group is generated by the cohomology of a quadric relative to hyperplanes, and that is a determinant...
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作者：Vasy, Andras
作者单位：Stanford University
摘要：In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under perturbations. This framework, described in Sect. 2, resides on a compact manifold without boundary, hence in the standard setting of microlocal analysis. Many natural applications arise in the setting of non-Riemannian b-metrics in the context of Melrose's b-structures. These include asymptotically de...
