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作者：Nelson, Paul D.
作者单位：Aarhus University
摘要：Let (pi, sigma) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan-Gross-Prasad pair (Un+1, U-n) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local con-ditions (in particular, temperedness). We prove that the subconvex bound L(pi x sigma, 1/2) << C(pi x sigma )(1/4-delta...
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作者：Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
作者单位：Norwegian University of Science & Technology (NTNU)
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作者：Italiano, Giovanni; Martelli, Bruno; Migliorini, Matteo
作者单位：Scuola Normale Superiore di Pisa
摘要：We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic.
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作者：Alper, Jarod; Halpern-Leistner, Daniel; Heinloth, Jochen
作者单位：University of Washington; University of Washington Seattle; Cornell University; University of Duisburg Essen
摘要：We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a T-stratification. These results provide a generalization of the Keel-Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to constr...
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作者：Ivanov, Sergei; Mamaev, Daniil; Nordskova, Anya
作者单位：Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; Hasselt University
摘要：We prove that if all intersections of a convex body B subset of R-4 with 3-dimensional linear subspaces are linearly equivalent then B is a centered ellipsoid. This gives an affirmative answer to the case n = 3 of the following question by Banach from 1932: Is a normed vector space V whose n-dimensional linear subspaces are all isometric, for a fixed 2 <= n < dim V, necessarily Euclidean? The dimensions n = 3 and dim V = 4 is the first case where the question was unresolved. Since the 3-sphere...
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作者：Lindenstrauss, E.; Mohammadi, A.
作者单位：Hebrew University of Jerusalem; University of California System; University of California San Diego
摘要：We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL2(R) in arithmetic quotients of SL2(C) and SL2(R) x SL2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.
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作者：Hundertmark, Dirk; Kunstmann, Peer; Ried, Tobias; Vugalter, Semjon
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Illinois System; University of Illinois Urbana-Champaign; Max Planck Society; Leipzig University
摘要：There are several proofs by now for the famous Cwikel-Lieb-Rozenblum (CLR) bound, which is a semiclassical bound on the number of bound states for a Schrodinger operator, proven in the 1970s. Of the rather distinct proofs by Cwikel, Lieb, and Rozenblum, the one by Lieb gives the best constant, the one by Rozenblum does not seem to yield any reasonable estimate for the constants, and Cwikel's proof is said to give a constant which is at least about 2 orders of magnitude off the truth. This situ...
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作者：Breuil, Christophe; Herzig, Florian; Hu, Yongquan; Morra, Stefano; Schraen, Benjamin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Toronto; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let p be a prime number, F a totally real number field unramified at places above p and D a quaternion algebra of center F split at places above p and at no more than one infinite place. Let v be a fixed place of F above p and r : Gal(F/F) ? GL(2)(F-p) an irreducible modular continuous Galois representation which, at the place v, is semisimple and sufficiently generic (and satisfies some weak genericity conditions at a few other finite places). We prove that many of the admissible smooth repre...
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作者：Ionescu, Alexandru D.; Magyar, Akos; Mirek, Mariusz; Szarek, Tomasz Z.
作者单位：Princeton University; University System of Georgia; University of Georgia; Rutgers University System; Rutgers University New Brunswick; University of Wroclaw; Basque Center for Applied Mathematics (BCAM)
摘要：We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on sigma-finite measure spaces. We also establish corresponding maximal inequalities on Lp for 1 <=infinity and rho-variational inequalities on L2 for 2
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作者：Bandeira, Afonso S. S.; Boedihardjo, March T. T.; van Handel, Ramon
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
摘要：A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices X = S-i g(i)A(i) where g(i) are independent standard Gaussian variables and A(i) are matrix coefficients. This bound exhibits a logarithmic dependence on dimension that is sharp when the matrices A(i) commute, but often proves to be suboptimal in the presence of noncommutativity. In this paper, we develop ...
