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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).
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作者：Pfitzner, Hermann
作者单位：Universite de Orleans
摘要：A boundary for a real Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is coarser than the weak topology on the Banach space. The boundary problem asks whether nevertheless both topologies have the same norm bounded compact sets. The main theorem of this paper states the equivalence of countable and sequential compactness of...
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作者：Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; Massachusetts Institute of Technology (MIT); Kobe University; University of California System; University of California Los Angeles
摘要：We consider the cubic defocusing nonlinear Schrodinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any delta << 1, K >> 1, s > 1, we construct smooth initial data u(0) with parallel to u(0)parallel to(s)(H) < delta, so that the corresponding time evolution u satisfies parallel to u(T)parallel to(Hs) > K at some time T. This...
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作者：Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; Van den Bergh, Michel
作者单位：Syracuse University; University of Toronto; University Toronto Scarborough; Hasselt University
摘要：We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.
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作者：Makarov, N.; Poltoratski, A.
作者单位：Texas A&M University System; Texas A&M University College Station; California Institute of Technology
摘要：We consider the family of Toeplitz operators T-J (S) over bara acting in the Hardy space H-2 in the upper halfplane; J and S are given meromorphic inner functions, and a is a real parameter. In the case where the argument of S has a power law type behavior on the real line, we compute the critical value c(J, S) = inf {a : ker T-J (S) over bara not equal 0}. The formula for c(J, S) generalizes the Beurling-Malliavin theorem on the radius of completeness for a system of exponentials.
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作者：Hausel, Tamas
作者单位：University of Oxford
摘要：We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
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作者：Merenkov, Sergei
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Motivated by questions in geometric group theory we define a quasisymmetric co-Hopfian property for metric spaces and provide an example of a metric SierpiAski carpet with this property. As an application we obtain a quasi-isometrically co-Hopfian Gromov hyperbolic space with a SierpiAski carpet boundary at infinity. In addition, we give a complete description of the quasisymmetry group of the constructed SierpiAski carpet. This group is uncountable and coincides with the group of bi-Lipschitz...
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作者：Popa, Sorin; Vaes, Stefaan
作者单位：KU Leuven; University of California System; University of California Los Angeles
摘要：We prove a unique crossed product decomposition result for group measure space II1 factors L-infinity(X) (sic) Gamma arising from arbitrary free ergodic probability measure preserving (p. m. p.) actions of groups Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T-n denotes the group of upper triangular matrices in PSL(n, Z), then any free, mixi...
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作者：Binyamini, Gal; Novikov, Dmitry; Yakovenko, Sergei
作者单位：Weizmann Institute of Science
摘要：We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing infinitesimal Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection defined over ae (the Gauss...
