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作者：Bayer, Arend; Macri, Emanuele
作者单位：University of Edinburgh; University System of Ohio; Ohio State University
摘要：We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space of stable sheaves on a K3 surface : (a) We describe the nef cone, the movable cone, and the effective cone of in terms of the Mukai lattice of . (b) We establish a long-standing conjecture that predicts the existence of a birational Lagrangian fibration on whenever admits an integral divisor class of square zero (with respect to the Beauville-Bogomolov form). T...
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作者：Antieau, Benjamin; Williams, Ben
作者单位：University of California System; University of California Los Angeles; University of Southern California
摘要：We show that, in general, over a regular integral noetherian affine scheme X of dimension at least 6, there exist Brauer classes on X for which the associated division algebras over the generic point have no Azumaya maximal orders over X. Despite the algebraic nature of the result, our proof relies on the topology of classifying spaces of algebraic groups.
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作者：Alazard, T.; Burq, N.; Zuily, C.
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider turn out to be only of -class for some and consequently have unbounded curvature, while the initial velocities are only Lipschitz. We reduce the system using a paradifferential approach.
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作者：Bauer, I.; Catanese, F.
作者单位：University of Bayreuth
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作者：Jia, Hao; Sverak, Vladimir
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
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作者：Spiess, Michael
作者单位：University of Bielefeld
摘要：Let E be a modular elliptic curve over a totally real number field F. We prove the weak exceptional zero conjecture which links a (higher) derivative of the p-adic L-function attached to E to certain p-adic periods attached to the corresponding Hilbert modular form at the places above p where E has split multiplicative reduction. Under some mild restrictions on p and the conductor of E we deduce the exceptional zero conjecture in the strong form (i.e. where the automorphic p-adic periods are r...
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作者：Iyama, Osamu; Wemyss, Michael
作者单位：Nagoya University; University of Edinburgh; Heriot Watt University
摘要：We first generalize classical Auslander-Reiten duality for isolated singularities to cover singularities with a one-dimensional singular locus. We then define the notion of CT modules for non-isolated singularities and we show that these are intimately related to noncommutative crepant resolutions (NCCRs). When R has isolated singularities, CT modules recover the classical notion of cluster tilting modules but in general the two concepts differ. Then, wanting to generalize the notion of NCCRs ...
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作者：Baranski, Krzysztof; Fagella, Nuria; Jarque, Xavier; Karpinska, Boguslawa
作者单位：University of Warsaw; University of Barcelona; Warsaw University of Technology
摘要：We prove that every transcendental meromorphic map f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton...
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作者：Benson, David J.; Grodal, Jesper; Henke, Ellen
作者单位：University of Aberdeen; University of Copenhagen
摘要：We show that if an inclusion of finite groups Ha parts per thousand currency signG of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd. This generalizes classical results of Quillen who proved this when H is a Sylow p-subgroup, and furthermore implies a hitherto difficult result of Mislin about cohomology isomorphisms. For p=2 we give analogous results, at the cost of replaci...
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作者：Bourgain, Jean; Kontorovich, Alex
作者单位：Institute for Advanced Study - USA; Yale University
摘要：We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.
