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作者：Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho
作者单位：Kyoto University; Seoul National University (SNU); Seoul National University (SNU); Kyung Hee University
摘要：Let J be a set of pairs consisting of good -modules and invertible elements in the base field . The distribution of poles of normalized R-matrices yields Khovanov-Lauda-Rouquier algebras for each . We define a functor from the category of graded -modules to the category of -modules. The functor sends convolution products of finite-dimensional graded -modules to tensor products of finite-dimensional -modules. It is exact if is of finite type A, D, E. If is the fundamental representation of of w...
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作者：Alvarez-Gavela, Daniel
作者单位：Stanford University
摘要：We establish a full h-principle (close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy.
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作者：Baldi, Pietro; Berti, Massimiliano; Haus, Emanuele; Montalto, Riccardo
作者单位：University of Naples Federico II; International School for Advanced Studies (SISSA); University of Zurich
摘要：We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutionsnamely periodic and even in the space variable xof a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the fully nonlinear nature of the gravity water waves equationsthe hi...
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作者：Wemyss, Michael
作者单位：University of Glasgow
摘要：Suppose that is a minimal model of a complete local Gorenstein 3-fold, where the fibres of f are at most one dimensional, so by Van den Bergh (Duke Math J 122(3):423-455, 2004) there is a noncommutative ring derived equivalent to X. For any collection of curves above the origin, we show that this collection contracts to a point without contracting a divisor if and only if a certain factor of is finite dimensional, improving a result of Donovan and Wemyss (Contractions and deformations, http://...
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作者：Hind, R.; Kerman, E.
作者单位：University of Notre Dame; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We correct here an error in the proof of Theorem 1.1 of our paper New obstructions to symplectic embeddings, henceforth referred to as [6].
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作者：Le Calvez, P.; Tal, F. A.
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universidade de Sao Paulo
摘要：This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and Brouwer theory. The main development is a novel theory of orbit forcing using maximal isotopies and transverse foliations. This allows us to derive new proofs for some known results as well as some new applications, among which we note the following: we extend Franks and Handel's classification of zero entropy maps of for non-wandering homeomorphisms; we show that if f is a Hamilto...
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作者：Kuhn, Nicholas J.
作者单位：University of Virginia
摘要：We study the Hurewicz map is the generalized homology theory associated to a connective commutative S-algebra R. We prove that the decreasing filtration of the domain associated to an R-based Adams resolution is compatible with a filtration of the range associated to the augmentation ideal filtration of the augmented commutative S-algebra. The proof of our main theorem makes much use of composition properties of this filtration and its interaction with Topological Andre-Quillen homology. An ap...
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作者：Abbondandolo, Alberto; Bramham, Barney; Hryniewicz, Umberto L.; Salomao, Pedro A. S.
作者单位：Ruhr University Bochum; Universidade Federal do Rio de Janeiro; Universidade de Sao Paulo
摘要：The systolic ratio of a contact form on the three-sphere is the quantity rho(sys)(alpha) = T-min(alpha)(2)/vol(S-3, alpha boolean AND d alpha), where is the minimal period of closed Reeb orbits on . A Zoll contact form is a contact form such that all the orbits of the corresponding Reeb flow are closed and have the same period. Our first main result is that in a neighbourhood of the space of Zoll contact forms on , with equality holding precisely at Zoll contact forms. This implies a particula...
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作者：Helm, David; Moss, Gilbert
作者单位：Imperial College London
摘要：We prove a descent criterion for certain families of smooth representations of modules (the so-called integral Bernstein center) in terms of Galois theory and the local Langlands correspondence. An immediate consequence is the conjectural local Langlands correspondence in families of Emerton and Helm (Ann Sci Ec Norm Super (4) 47(4):655-722, 2014).
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作者：Buhovsky, Lev; Humiliere, Vincent; Seyfaddini, Sobhan
作者单位：Tel Aviv University; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critical points of a smooth function on M. It is well known that the Arnold conjecture holds for Hamiltonian homeomorphisms of closed symplectic surfaces. The goal of this paper is to provide a counterexample to the Arnold conjecture for Hamiltonian homeomorphisms in dimensions four and higher. More precisely, we prove tha...
