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作者：Li, Jialun; Pan, Wenyu
作者单位：University of Zurich; University of Chicago
摘要：Let Gamma be a geometrically finite discrete subgroup in SO(d + 1, 1)degrees with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle T-1 (Gamma\Hd+1) with respect to the Bowen-Margulis- Sullivan measure, which is the unique probability measure on T-1 (Gamma\Hd+1) with maximal entropy. As an application, we obtain a resonance-free region for the resolvent of the Laplacian on Gamma\Hd+1. Our approach is to construct a coding for the geodesic flow ...
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作者：Bright, Martin; Newton, Rachel
作者单位：University of London; King's College London
摘要：Classifying elements of the Brauer group of a variety X over a p-adic field by the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by Kato's Swan conductor. The refined Swan conductor con-trols how the evaluation maps vary on p-adic discs: this provides a geometric char-acterisation of the refined Swan conductor. We give applications to rational points on varieties over number fields, including failure of weak approximation for vari...
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作者：Gunningham, Sam; Jordan, David; Safronov, Pavel
作者单位：Montana State University System; Montana State University Bozeman; University of Edinburgh; University of Zurich
摘要：We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that skein modules of closed 3-manifolds are finite-dimensional, resolving in the affirmative a conjecture of Witten.
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作者：Banks, William; Ford, Kevin; Tao, Terence
作者单位：University of Missouri System; University of Missouri Columbia; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Los Angeles
摘要：We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we obtain heuristic upper and lower bounds for the size of the largest prime gap in the interval [1, x]. Our results are stated in terms of the extremal bounds in the interval sieve problem. The same methods also allow us to rigorously relate the validity of th...
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作者：Berti, Massimiliano; Hassainia, Zineb; Masmoudi, Nader
作者单位：International School for Advanced Studies (SISSA); New York University; New York University Abu Dhabi; New York University
摘要：We prove the existence of time quasi-periodic vortex patch solutions of the 2d-Euler equations in R2, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full Lebesgue measure. The problem is reformulated into a quasi-linear Hamiltonian equation for a radial displacement from the ellipse. A major difficulty of the KAM proof is the presence of a zero normal mode frequency, which is due to the conservation of the angular momentum. Th...
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作者：Ivorra, Florian; Sebag, Julien
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let k be a field of characteristic zero and let X be an algebraic k-variety endowed with an action of the multiplicative algebraic monoid A(1). In this article, we prove that the nearby motivic sheaf functor of a weighted A(1)-equivariant function on X commutes with direct (and exceptional direct) images when applied to constant objects and their twists by Thom spaces of equivariant vector bundles. This proves a generalized categorified version of the conjectures of Behrend-Bryan-Szendro?i and...
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作者：Guo, Yan; Pausader, Benoit; Widmayer, Klaus
作者单位：Brown University; University of Zurich; University of Vienna
摘要：We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform rigid body rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. To establish this, we introduce a framework that builds on the symmetries of the problem and precisely captures the anisotropic, dispersive mechanism due to rotation. This enables a fine analysis...
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作者：Bary-Soroker, Lior; Koukoulopoulos, Dimitris; Kozma, Gady
作者单位：Tel Aviv University; Universite de Montreal; Weizmann Institute of Science
摘要：Let mu be a probability measure on Z that is not a Dirac mass and that has finite support. We prove that if the coefficients of a monic polynomial f (x) is an element of Z[x] of degree n are chosen independently at random according to mu while ensuring that f (0) not equal 0, then there is a positive constant theta = theta (mu) such that f (x) has no divisors of degree <= theta n with probability that tends to 1 as n -> infinity. Furthermore, in certain cases, we show that a random polynomial ...
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作者：Mooney, Connor; Yang, Yang
作者单位：University of California System; University of California Irvine
摘要：We construct nonlinear entire anisotropic minimal graphs over R-4, completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over R-n, n >= 8.
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作者：De Filippis, Cristiana; Mingione, Giuseppe
作者单位：University of Parma
摘要：Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are locally Holder continuous if so are their coefficients.
