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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 ...
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作者：Colin, Vincent; Dehornoy, Pierre; Rechtman, Ana
作者单位：Nantes Universite; Ecole Centrale de Nantes; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we obtain that on a closed 3-manifold, every nondegenerate Reeb vector field has either two or infinitely many periodic orbits, and two periodic orbits are possible only on the tight sphere or on a tight lens space. Moreover we get that if M is a closed oriented 3-manifold that is not a graph manifold, for example a hyperbolic manifold, then every nondegenerate Reeb vector...
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作者：Liu, Yi
作者单位：Peking University
摘要：For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.
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作者：Greene, Joshua Evan; Lobb, Andrew
作者单位：Boston College; Durham University
摘要：For every smooth Jordan curve gamma and cyclic quadrilateral Q in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of Q to gamma. The proof relies on the theorem of Polterovich and Viterbo that an embedded Lagrangian torus in C-2 has minimum Maslov number 2.
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作者：Bamler, Richard H.
作者单位：University of California System; University of California Berkeley
摘要：We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows, , 2020). Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric flow. We will study the geometric and analytic properties of this limiting flow, as well as the convergence...
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作者：Solecki, Slawomir
作者单位：Cornell University
摘要：We show that, for a generic measure preserving transformation T, the closed group generated by T is not isomorphic to the topological group L-0(lambda, T) of all Lebesgue measurable functions from [0, 1] to T (taken with pointwise multiplication and the topology of convergence in measure). This result answers a question of Glasner and Weiss. The main step in the proof consists of showing that Koopman representations of ergodic boolean actions of L-0(lambda, T) possess a non-trivial spectral pr...
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作者：Tsuzuki, Nobuo
作者单位：Tohoku University
摘要：The minimal slope conjecture, which was proposed by K. S. Kedlaya, asserts that two irreducible overconvergent F-isocrystals on a smooth variety are isomorphic to each other if both minimal slope constitutions of slope filtrations are isomorphic to each other. We affirmatively solve the minimal slope conjecture for overconvergent F-isocrystals on curves and for overconvergent (Q) over bar (p)-F-isocrystals on smooth varieties over finite fields.
