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作者：Benoist, Y
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
摘要：Let Omega be an indecomposable properly convex open subset of the real projective 3-space which is divisible i.e. for which there exists a torsion free discrete group Gamma of projective transformations preserving Omega such that the quotient M := Gamma\Omega is compact. We study the structure of M and of partial derivative Omega, when Omega is not strictly convex: The union of the properly embedded triangles in Omega projects in M onto an union of finitely many disjoint tori and Klein bottles...
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作者：Gan, SB; Wen, L
作者单位：Peking University
摘要：We give an affirmative answer to a problem of Liao and Mane which asks whether, for a nonsingular flow to loose the Omega-stability, it must go through a critical-element-bifurcation. More precisely, a vector field S on a compact boundaryless manifold is called a star system if S has a C-1 neighborhood U in the set of C-1 vector fields such that every singularity and every periodic orbit of every X epsilon U is hyperbolic. We prove that any nonsingular star flow satisfies Axiom A and the no cy...
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作者：Ding, Weiyue; Li, Jiayu; Liu, Qingyue
作者单位：Peking University; Chinese Academy of Sciences; Abdus Salam International Centre for Theoretical Physics (ICTP); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
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作者：Bruinier, JH; Yang, TH
作者单位：University of Cologne; University of Wisconsin System; University of Wisconsin Madison
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作者：Bezrukavnikov, Roman
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. It turns out to be related to irreducible objects in the heart of a certain t-structure on the derived category of equivariant coherent sheaves on the Springer resolution, and to equivariant coherent IC sheaves on the nil-cone. The support of the cohomology is described in terms of cells in affine Weyl groups. The basis in the Grot...
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作者：Bringmann, Kathrin; Ono, Ken
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for N-e(n) (resp. N-o(n)), the number of partitions of n with even (resp. odd) rank. Thanks to Rademacher's celebrated formula for the partition function, this problem is equivalent to that of obtaining a formula for the coefficients of the mock theta function f(q), a problem with its own long history dating to Ramanujan's last letter to Hardy. Little was known a...
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作者：Brubaker, Ben; Bump, Daniel; Friedberg, Solomon
作者单位：Stanford University; Boston College
摘要：To each reduced root system Phi of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Phi. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each...
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作者：Marinescu, G; Dinh, TC
作者单位：Humboldt University of Berlin; Universite Paris Saclay; Institute of Mathematics of the Romanian Academy; University of Bucharest; Romanian Academy
摘要：We show that the 'pseudoconcave holes' of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension two. As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel's theorems to dimension two.
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作者：Hampton, M; Moeckel, R
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.
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作者：Knutson, Allen; Miller, Ezra; Shimozono, Mark
作者单位：University of California System; University of California Berkeley; Virginia Polytechnic Institute & State University
摘要：We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton [BF99 ]. All four formulae are combinatorial, in the sense that they are expressed in terms of combinatorial objects of certain types: Zelevinsky permutations, lacing diagrams, Young tableaux, and pipe dreams (also known as rc-graphs). Three of our formulae are multiplicity-free and geometric, meaning that their summands have coefficient 1 and correspond bijectively to components of a torus-invar...
