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作者：De Simoi, Jacopo; Kaloshin, Vadim; Leguil, Martin
作者单位：University of Toronto; Institute of Science & Technology - Austria; Universite de Picardie Jules Verne (UPJV); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Geneva; Imperial College London
摘要：We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case...
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作者：Bakker, Benjamin; Brunebarbe, Yohan; Tsimerman, Jacob
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Bordeaux; University of Toronto
摘要：We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic spaces and coherent sheaves that are definable with respect to a given o-minimal structure, and prove a GAGA-type theorem algebraizing definable coherent sheaves on complex algebraic spaces. We then combine this with algebraization theorems of Artin to show that proper definable images of complex ...
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作者：Isenrich, Claudio Llosa; Py, Pierre
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：We prove that in a cocompact complex hyperbolic arithmetic lattice Gamma < PU(m, 1) of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to Z with kernel of type Fm-1 but not of type F-m. This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method also yields a proof of a special case of Singer's conjecture for aspherical Kahler manifolds.
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作者：Li, Yingkun
作者单位：Technical University of Darmstadt
摘要：In this paper, we investigate the algebraic nature of the value of a higher Green function on an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of Gross and Zagier in the setting of higher Green functions on the product of two modular curves. In the process, we will study analogue of harmonic Maass forms in the setting of Hilbert modular forms, and obtain results concerning the arithmetic of their holomorphic part Fourier coefficients. As a consequence, we a...
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作者：Fujiwara, Koji; Sela, Zlil
作者单位：Kyoto University; Hebrew University of Jerusalem
摘要：We study the countable set of rates of growth of a hyperbolic group with respect to all its finite generating sets. We prove that the set is well-ordered, and that every real number can be the rate of growth of at most finitely many generating sets up to automorphism of the group. We prove that the ordinal of the set of rates of growth is at least omega(omega 0)(0), and in case the group is a limit group (e.g. free and surface groups) it is omega(omega 0)(0). We further study the rates of grow...
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作者：Novack, Matthew; Vicol, Vlad
作者单位：Purdue University System; Purdue University; New York University
摘要：For any regularity exponent beta < 1/2, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class C-t(0)(H-beta & cap; L1/(1-2 beta)). By interpolation, such solutions belong to (CtB3,infinity S)-B-0 for s approaching 1/3 as beta approaches 1/2. Hence this result provides a new proof of the flexible side of the L3-based Onsager conjecture. Of equal importance is that the intermittent nature of our solutions matches that of turbulent flows, which are obs...
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作者：Gan, Wee Teck; Savin, Gordan
作者单位：National University of Singapore; Utah System of Higher Education; University of Utah
摘要：We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is the exceptional group G(2). We prove the Howe duality conjecture for these dual pairs and a dichotomy theorem, and determine explicitly the theta lifts of all non-cuspidal representations.
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作者：Bresciani, Giulio
摘要：Let X be a curve over a field k finitely generated over Q and t an indeterminate. We prove that, if s is a section of pi(1)(X) -> Gal(k) such that the base change s(k(t)) is birationally liftable, then s comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.
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作者：Bader, Uri; Fisher, David; Miller, Nicholas; Stover, Matthew
作者单位：Weizmann Institute of Science; Rice University; University of Oklahoma System; University of Oklahoma - Norman; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：For n >= 2, we prove that a finite volume complex hyperbolic n-manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of real dimension at least two is arithmetic, paralleling our previous work for real hyperbolic manifolds. As in the real hyperbolic case, our primary result is a superrigidity theorem for certain representations of complex hyperbolic lattices. The proof requires developing new general tools not needed in the real hyperbolic case. Our main r...
