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作者：Eichinger, Benjamin; Lukic, Milivoje; Simanek, Brian
作者单位：Lancaster University; Technische Universitat Wien; Rice University; Baylor University
摘要：We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel- Darboux kernel and the realization that bulk universality for thi...
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作者：Yuan, Xinyi
作者单位：Peking University
摘要：In this paper, we construct the admissible canonical bundle of a quasi-projective family of curves, prove that it is a big adelic line bundle when the family has maximal variation, and apply it to prove a uniform Bogomolovtype theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Vojta, Dimitrov-Gao-Habegger and Kuhne. Our treatment is based on the theory of adelic line bundles on quasi-projective varieties r...
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作者：Chaika, Jon; Smillie, John; Weiss, Barak
作者单位：Rice University; University of Warwick; Tel Aviv University
摘要：We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horo cycle flow orbits Uq in strata of translation surfaces. In the genus 2 stratum H(1, 1) we find orbits Uq which are generic for a measure whose support is strictly contained in Uq and find orbits which are not generic for any measure. We also describe a horo cycle orbit-closure whose Hausdorff dimension is not an integer.
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作者：Eichinger, Benjamin; Lukic, Milivoje; Simanek, Brian
作者单位：Lancaster University; Technische Universitat Wien; Rice University; Baylor University
摘要：We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel- Darboux kernel and the realization that bulk universality for thi...
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作者：Yuan, Xinyi
作者单位：Peking University
摘要：In this paper, we construct the admissible canonical bundle of a quasi-projective family of curves, prove that it is a big adelic line bundle when the family has maximal variation, and apply it to prove a uniform Bogomolovtype theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Vojta, Dimitrov-Gao-Habegger and Kuhne. Our treatment is based on the theory of adelic line bundles on quasi-projective varieties r...
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作者：Chaika, Jon; Smillie, John; Weiss, Barak
作者单位：Rice University; University of Warwick; Tel Aviv University
摘要：We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horo cycle flow orbits Uq in strata of translation surfaces. In the genus 2 stratum H(1, 1) we find orbits Uq which are generic for a measure whose support is strictly contained in Uq and find orbits which are not generic for any measure. We also describe a horo cycle orbit-closure whose Hausdorff dimension is not an integer.
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作者：Newton, James; Thorne, Jack
作者单位：University of Oxford; University of Cambridge
摘要：Let F be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of GL2(AF) associated to Hilbert modular forms of regular weight.
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作者：Berger, Pierre
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points that are not conjugate to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen to be ergodic or, to the contrary, with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solves a problem of Herman (1998). One aspect of the proof provides a new approximation theorem; it enables the implementation ...
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作者：Karpeshina, Yulia; Parnovski, Leonid; Shterenberg, Roman
作者单位：University of Alabama System; University of Alabama Birmingham; University College London; University of London; University College London
摘要：We consider Schro & uml;dinger operators H = -triangle + V (x) in Rd, d >= 2, with quasi-periodic potentials V (x). We prove that the absolutely continuous spectrum of a generic H contains a semi-axis [lambda & lowast;, +infinity). We also construct a family of eigenfunctions of the absolutely continuous spectrum; these eigenfunctions are small perturbations of the exponentials. The proof is based on a version of the multi-scale analysis in the momentum space with several new ideas introduced ...
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作者：Pan, Lue
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves with infinite level at p in both holomorphic and anti-holomorphic directions. As applications, we reprove a classicality result of Emerton which says that every absolutely irreducible two dimensional Galois representation that is regular de Rham at p and appears in the completed cohomology of modular curves comes from a...
