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作者：Guth, Larry
作者单位：University of Toronto
摘要：We prove the endpoint case of the multilinear Kakeya conjecture of Bennett, Carbery and Tao. The proof uses the polynomial method introduced by Dvir.
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作者：Lam, Thomas; Shimozono, Mark
作者单位：University of Michigan System; University of Michigan; Virginia Polytechnic Institute & State University
摘要：Let G be a simple and simply-connected complex algebraic group, P aS,aEuro parts per thousand G a parabolic subgroup. We prove an unpublished result of D. Peterson which states that the quantum cohomology QH (*)(G/P) of a flag variety is, up to localization, a quotient of the homology H (*)(Gr (G) ) of the affine Grassmannian Gr (G) of G. As a consequence, all three-point genus-zero Gromov-Witten invariants of G/P are identified with homology Schubert structure constants of H (*)(Gr (G) ), est...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we characterize the set S of all points that are connected to the root by more than one geodesic. The set S is dense in the Brownian map and homeomorphic to a non-compact real tree. Furthermore, for every x in S, the number of distinct geodesics from x to the roo...
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作者：Boucksom, Sebastien; Eyssidieux, Philippe; Guedj, Vincent; Zeriahi, Ahmed
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Aix-Marseille Universite
摘要：We define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kahler manifold X. Given a big (1, 1)-cohomology class alpha on X (i.e. a class that can be represented by a strictly positive current) and a positive measure mu on X of total mass equal to the volume of alpha and putting no mass on pluripolar sets, we show that mu can be written in a unique way as the top-degree self-intersection in the non-pluripolar sense of a closed positive current in ...
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作者：Garban, Christophe; Pete, Gabor; Schramm, Oded
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); University of Toronto; Microsoft
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作者：Ikromov, Isroil A.; Kempe, Michael; Mueller, Detlef
作者单位：Samarkand State University; University of Kiel
