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作者：Zhu, Xinwen
摘要：We endow the set of lattices in Q(P)(n) with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake equivalence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
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作者：Naber, Aaron; Valtora, Daniele
摘要：In this paper we study the regularity of stationary and minimizing harmonic maps f: B-2(p) subset of M -> N between Riemannian manifolds. If Sk(f)={x is an element of M: no tangent map at x is k+1-symmetric} is kth-stratum of the singular set of f, then it is well known that dimSk=k, however little else about the structure of Sk(f) is understood in any generality. Our first result is for a general stationary harmonic map, where we prove that Sk(f) is k-rectifiable. In the case of minimizing ha...
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作者：Tikuisis, Aaron; White, Stuart; Winter, Wilhelm
摘要：We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear C*-algebras of finite nuclear dimension which satisfy the UCT is now complete. Secondly, our result links the finite to the general version of the Toms-Winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dim...
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作者：Labourie, Francois
摘要：We prove that given a Hitchin representation in a real split rank 2 group G(0), there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin components by a Hermitian bundle over Teichm\uller space. The proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of G(0). Some partial extensions of the construction hold for cyclic bundles in higher rank.
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作者：Kowalski, Emmanuel; Michel, Philippe; Sawin, Will
摘要：We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cusp forms twisted by characters modulo primes, and to the distribution in arithmetic progressions to large moduli of certain Eisenstein-Hecke coefficients on GL(3). Our main tools are new bounds for certain complete sums in three variables over...
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作者：[Anonymous]
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作者：Koziarz, Vincent; Maubon, Julien
摘要：Let rho be a maximal representation of a uniform lattice Gamma subset of SU(n , 1), n >= 2, in a classical Lie group of Hermitian type G. We prove that necessarily G = SU(p, q) with p >= qn and there exists a holomorphic or antiholomorphic rho-equivariant map from the complex hyperbolic n-space to the symmetric space associated to SU(p, q). This map is moreover a totally geodesic homothetic embedding. In particular, up to a representation in a compact subgroup of SU(p, q), the representation p...
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作者：Krieger, Joachim; Tataru, Daniel
摘要：We consider the hyperbolic Yang-Mills equation on the Minkowski space R4+1. Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem.
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作者：Binyamini, Gal; Novikov, Dmitry
摘要：We consider the structure R-RE obtained from (R, <, +, ) by adjoining the restricted exponential and sine functions. We prove Wilkie's conjecture for sets definable in this structure: the number of rational points of height H in the transcendental part of any definable set is bounded by a polynomial in log H. We also prove two refined conjectures due to Pila concerning the density of algebraic points from a fixed number field, or with a fixed algebraic degree, for RE-definable sets.
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作者：Bedrossian, Jacob; Germain, Pierre; Masmoudi, Nader
摘要：We study Sobolev regularity disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. Our goal is to estimate how the stability threshold scales in Re: the largest the initial perturbation can be while still resulting in a solution that does not transition away from Couette flow. In this work we prove that initial data that satisfies parallel to u(in)parallel to H-sigma <= delta Rc(-3/2) for any sigma > 9/2 and some delta = de...
