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作者：Boutillier, Cedric; de Tiliere, Beatrice; Raschel, Kilian
作者单位：Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite de Tours
摘要：We introduce a one-parameter family of massive Laplacian operators (Delta(m(k)))(k is an element of(0,1)) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for the inverse of Delta(m(k)) , the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the corresponding statistical mechanics model of random rooted spanning forests. We prove an explicit local formula f...
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作者：Gilmer, Patrick M.; Masbaum, Gregor
作者单位：Louisiana State University System; Louisiana State University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：For a prime, and an integer, we use Topological Quantum Field Theory (TQFT) to study a family of highest weight modules for the symplectic group where K is an algebraically closed field of characteristic p. This permits explicit formulae for the dimension and the formal character of for these highest weights.
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作者：Faure, Frederic; Tsujii, Masato
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Kyushu University
摘要：We consider the semi-classical (or Gutzwiller-Voros) zeta functions for contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small , its zeros are contained in the union of the -neighborhood of the imaginary axis, , and the half-plane , up to finitely many exceptions, where is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogu...
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作者：Hochman, Michael; Solomyak, Boris
作者单位：Hebrew University of Jerusalem
摘要：Let mu be a measure on SL2(R) generating a non-compact and totally irreducible subgroup, and let nu be the associated stationary (Furstenberg) measure for the action on the projective line. We prove that if mu is supported on finitely many matrices with algebraic entries, then dim nu = min {1, h(RW)(mu)/2 chi(mu)} where h(RW)(mu) is the random walk entropy of mu, chi(mu) is the Lyapunov exponent for the random matrix product associated with mu, and dim denotes pointwise dimension. In particula...
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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.
