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作者：Rajala, Kai
作者单位：University of Jyvaskyla
摘要：We establish uniformization results for metric spaces that are homeomorphic to the Euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and sufficient condition for such spaces to be QC equivalent to the Euclidean plane, disk, or sphere. Moreover, we show that if such a QC parametrization exists, then the dilatation can be bounded by 2. As an application, we show that the Euclidean upper bound for mea...
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作者：Bhatt, Bhargav; Scholze, Peter
作者单位：University of Michigan System; University of Michigan; University of Bonn
摘要：We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in for a perfect field k of characteristic p, is representable by an ind-(perfect scheme) over k. This improves on previous results of Zhu by constructing a natural ample line bundle. Along the way, we establish various foundational results on perfect schemes, notably h-descent results for vector bundles.
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作者：Saito, Takeshi
作者单位：University of Tokyo
摘要：We define the characteristic cycle of an ,tale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula A la Milnor for the total dimension of the space of vanishing cycles and an index formula computing the Euler-Poincar, characteristic, generalizing the Grothendieck-Ogg-Shafarevich formula to higher dimension. An essential ingredient of the construction and the proof is a partial gener...
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作者：Radeschi, Marco; Wilking, Burkhard
作者单位：University of Munster
摘要：We define a Besse manifold as a Riemannian manifold (M, g) all of whose geodesics are closed. A conjecture of Berger states that all prime geodesics have the same length for any simply connected Besse manifold. We firstly show that the energy function on the free loop space of a simply connected Besse manifold is a perfect Morse-Bott function with respect to a suitable cohomology. Secondly we explain when the negative bundles along the critical manifolds are orientable. These two general resul...
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作者：Dyatlov, Semyon; Zworski, Maciej
作者单位：Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.
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作者：McMullen, Curtis T.; Mohammadi, Amir; Oh, Hee
作者单位：Harvard University; University of California System; University of California San Diego; Yale University; Korea Institute for Advanced Study (KIAS)
摘要：This paper initiates the study of rigidity for immersed, totally geodesic planes in hyperbolic 3-manifolds M of infinite volume. In the case of an acylindrical 3-manifold whose convex core has totally geodesic boundary, we show that the closure of any immersed geodesic plane is a properly immersed submanifold of M. On the other hand, we show that rigidity fails for quasifuchsian manifolds.
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作者：McCammond, Jon; Sulway, Robert
作者单位：University of California System; University of California Santa Barbara
摘要：This article resolves several long-standing conjectures about Artin groups of Euclidean type. Specifically we prove that every irreducible Euclidean Artin group is a torsion-free centerless group with a decidable word problem and a finite-dimensional classifying space. We do this by showing that each of these groups is isomorphic to a subgroup of a group with an infinitet-ype Garside structure. The Garside groups involved are introduced here for the first time. They are constructed by applying...
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作者：Nemethi, Andras
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Eotvos Lorand University; Basque Center for Applied Mathematics (BCAM)
摘要：We prove that the link of a complex normal surface singularity is an L-space if and only if the singularity is rational. This via a result of Hanselman et al. (Taut foliations on graph manifolds, 2015. arXiv: 1508.0591), proving the conjecture of Boyer et al. (Math Ann 356(4): 1213-1245, 2013), shows that a singularity link is not rational if and only if its fundamental group is left-orderable if and only if it admits a coorientable taut foliation.
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作者：Mirzakhani, Maryam; Wright, Alex
作者单位：Stanford University
摘要：We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.
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作者：Phong, Duong H.; Picard, Sebastien; Zhang, Xiangwen
作者单位：Columbia University; University of California System; University of California Irvine
摘要：The Fu-Yau equation is an equation introduced by Fu and Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter . The equation was solved in dimension 2 by Fu and Yau in two successive papers for , and for . In the present paper, we solve the Fu-Yau equation in arbitrary dimension for . To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater ...
