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作者：Parnovski, Leonid; Sobolev, Alexander V.
作者单位：University of London; University College London
摘要：We consider a periodic self-adjoint pseudo-differential operator H=(-Delta) (m) +B, m > 0, in ae (d) which satisfies the following conditions: (i) the symbol of B is smooth in x, and (ii) the perturbation B has order less than 2m. Under these assumptions, we prove that the spectrum of H contains a half-line. This, in particular implies the Bethe-Sommerfeld conjecture for the Schrodinger operator with a periodic magnetic potential in all dimensions.
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作者：Caffarelli, Luis A.; Souganidis, Panagiotis E.
作者单位：University of Texas System; University of Texas Austin; University of Chicago
摘要：We establish a logarithmic-type rate of convergence for the homogenization of fully nonlinear uniformly elliptic second-order pde in strongly mixing media with similar, i.e., logarithmic, decorrelation rate. The proof consists of two major steps. The first, which is actually the only place in the paper where probability plays a role, establishes the rate for special (quadratic) data using the methodology developed by the authors and Wang to study the homogenization of nonlinear uniformly ellip...
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作者：Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony
作者单位：University of Toronto; Stanford University; Columbia University
摘要：We categorify the R-matrix isomorphism between tensor products of minuscule representations of U-q (sl(n)) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of U-q (sl(2)) which are related to representations of U-q (sl(n)) by quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometr...
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作者：Ressayre, N.
作者单位：Universite de Montpellier
摘要：Let G be a connected reductive subgroup of a complex connected reductive group (G) over cap. Fix maximal tori and Borel subgroups of G and (G) over cap. Consider the cone LR( G, (G) over cap) generated by the pairs (v, (v) over cap) of dominant characters such that V-v*. is a submodule of V (v) over cap. ( with usual notation). Here we give a minimal set of inequalities describing LR(G, (G) over cap) as a part of the dominant chamber. In other words, we describe the facets of LR(G, (G) over ca...
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作者：Junge, Marius; Xu, Quanhua
作者单位：Universite Marie et Louis Pasteur; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Following Grothendieck's characterization of Hilbert spaces we consider operator spaces F such that both F and F* completely embed into the dual of a C*-algebra. Due to Haagerup/Musat's improved version of Pisier/Shlyakhtenko's Grothendieck inequality for operator spaces, these spaces are quotients of subspaces of the direct sum C circle plus R of the column and row spaces (the corresponding class being denoted by QS(C circle plus R)). We first prove a representation theorem for homogeneous F ...
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作者：Smillie, John; Weiss, Barak
作者单位：Ben-Gurion University of the Negev; Cornell University
摘要：We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other characterizations of the lattice property.
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作者：Giordano, Thierry; Matui, Hiroki; Putnam, Ian F.; Skau, Christian F.
作者单位：Chiba University; University of Ottawa; University of Victoria; Norwegian University of Science & Technology (NTNU)
摘要：We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up to orbit equivalence of minimal dynamical systems on the Cantor set to include AF relations and acurrency sign (d) -actions.
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作者：Mazur, B.; Rubin, K.
作者单位：Harvard University; University of California System; University of California Irvine
摘要：In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find many twists with trivial Mordell-Weil group, and (assuming the Shafarevich-Tate conjecture) many other...
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作者：Ng, Lenhard
作者单位：Duke University
摘要：We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary number of positive punctures. The construction uses ideas from string topology.
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作者：Diverio, Simone; Merker, Joel; Rousseau, Erwan
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Sapienza University Rome; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We show that for every smooth projective hypersurface X subset of Pn+1 of degree d and of arbitrary dimension n >= 2, if X is generic, then there exists a proper algebraic subvariety Y not subset of X such that every nonconstant entire holomorphic curve f : C -> X has image f (C) which lies in Y, as soon as its degree satisfies the effective lower bound d >= 2(n5).
