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作者：Alper, Jarod; Fedorchuk, Maksym; Smyth, David Ishii
作者单位：Universidad de los Andes (Colombia); Columbia University; Harvard University
摘要：We prove that a generic canonically or bicanonically embedded smooth curve has semistable mth Hilbert points for all ma parts per thousand yen2. We also prove that a generic bicanonically embedded smooth curve has stable mth Hilbert points for all ma parts per thousand yen3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with -action, namely the canonically embedded balanced ribbon and the canonically embedded balanced double A (2...
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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：Mischler, Stephane; Mouhot, Clement
作者单位：Universite PSL; Universite Paris-Dauphine; University of Cambridge
摘要：This paper is devoted to the study of propagation of chaos and mean-field limits for systems of indistinguishable particles, undergoing collision processes. The prime examples we will consider are the many-particle jump processes of Kac and McKean (Kac in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955, Vol. III, pp. 171-197, 1956; McKean in J. Comb. Theory 2:358-382, 1967) giving rise to the Boltzmann equation. We solve the conjecture raised b...
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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：Hartl, Urs
作者单位：University of Munster
摘要：In their book, Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of p-divisible groups to some of these period spaces. They conjectured the existence of an ,tale bijective morphism of rigid analytic spaces and of a universal local system of ae (p) -vector spaces on . Such a local system would give rise to a tower of ,tale covering spaces of , equipped with a Hecke-action, and an action of the automorphism...
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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：Blomer, Valentin
摘要：We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behavior of the test functions on both sides. Applications to Weyl's law, exceptional eigenvalues, a large sieve and L-functions are given.
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作者：de Fernex, Tommaso
作者单位：Utah System of Higher Education; University of Utah
摘要：We prove that for Na parts per thousand yen4, all smooth hypersurfaces of degree N in a(TM) (N) are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals.
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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 ...
