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作者：Rondigs, Oliver; Spitzweck, Markus; Ostvaer, Paul Arne
摘要：We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice spectral sequence.
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作者：Luk, Jonathan; Oh, Sung-Tin
摘要：This is the first and main paper of a two-part series, in which we prove the C-2-formulation of the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended asymptotically flat data. For this model, it is known through the works of Dafermos and Dafermos-Rodnianski that the maximal globally hyperbolic future development of any admissible two-ended asymptotically flat Cauchy initial data set possesses a non-empty Cauchy horizon, ...
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作者：Buckmaster, Tristan; Vicol, Vlad
摘要：For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Holder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of fin...
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作者：Matveev, Konstantin
摘要：We prove the classification of homomorphisms from the algebra of sym- metric functions to R with non-negative values on Macdonald symmetric functions P-lambda, which was conjectured by S. V. Kerov in 1992.
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作者：Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent
摘要：We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their random-cluster representations. More precisely, we prove that For the Potts model on transitive graphs, correlations decay exponentially fast for beta < beta(c.) For the random-cluster model with cluster weight q >= 1 on transitive graphs, correlations decay exponential...
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作者：Frisch, Joshua; Hartman, Yair; Tamuz, Omer; Ferdowsi, Pooya Vahidi
摘要：A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure mu on G, it holds that all bounded mu-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, ...
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作者：Guillarmou, Colin; Lefeuvre, Thibault
摘要：In all dimensions, we prove that the marked length spectrum of a Riemannian manifold (M, g) with Anosov geodesic flow and non-positive curvature locally determines the metric in the sense that two close enough metrics with the same marked length spectrum are isometric. In addition, we provide a new stability estimate quantifying how the marked length spectrum controls the distance between the isometry classes of metrics. In dimension 2 we obtain similar results for general metrics with Anosov ...
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作者：Killip, Rowan; Visan, Monica
摘要：We prove global well-posedness of the Korteweg-de Vries equation for initial data in the space H-1 (R). This is sharp in the class of H-s (R) spaces. Even local well-posedness was previously unknown for s < -3/4. The proof is based on the introduction of a new method of general applicability for the study of low-regularity well-posedness for integrable PDE, informed by the existence of commuting flows. In particular, as we will show, completely parallel arguments give a new proof of global wel...
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作者：Khayutin, Ilya
摘要：We prove the mixing conjecture of Michel and Venkatesh for toral packets with negative fundamental discriminants and split at two fixed primes, assuming all splitting fields have no exceptional Landau-Siegel zero. As a consequence we establish for arbitrary products of indefinite Shimura curves the equidistribution of Galois orbits of generic sequences of CM points all of whose components have the same fundamental discriminant, assuming the CM fields are split at two fixed primes and have no e...
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作者：Binyamini, Gal; Novikov, Dmitry
摘要：We introduce the notion of a complex cell, a complexification of the cells/cylinders used in real tame geometry. For delta is an element of (0, 1) and a complex cell C, we define its holomorphic extension C subset of C-delta, which is again a complex cell. The hyperbolic geometry of C within C-delta provides the class of complex cells with a rich geometric function theory absent in the real case. We use this to prove a complex analog of the cellular decomposition theorem of real tame geometry....
