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作者：Castella, Francesc; Grossi, Giada; Lee, Jaehoon; Skinner, Christopher
作者单位：University of California System; University of California Santa Barbara; Korea Advanced Institute of Science & Technology (KAIST); Princeton University
摘要：Let E/Q be an elliptic curve and p an odd prime where E has good reduction, and assume that E admits a rational p-isogeny. In this paper we study the anticyclotomic Iwasawa theory of E over an imaginary quadratic field in which p splits, which we relate to the anticyclotomic Iwasawa theory of characters by a variation of the method of Greenberg-Vatsal. As a result of our study we obtain proofs (under relatively mild hypotheses) of PerrinRiou's Heegner point main conjecture, a p-converse to the...
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作者：Bate, David
作者单位：University of Warwick
摘要：We characterise rectifiable subsets of a complete metric space X in terms of local approximation, with respect to the Gromov-Hausdorff distance, by an n-dimensional Banach space. In fact, if E subset of X with H-n (E) < infinity and has positive lower density almost everywhere, we prove that it is sufficient that, at almost every point and each sufficiently small scale, E is approximated by a bi-Lipschitz image of Euclidean space. We also introduce a generalisation of Preiss's tangent measures...
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作者：Aizenbud, Avraham; Avni, Nir; Rubio, Roberto
作者单位：Weizmann Institute of Science; Northwestern University; University of Barcelona; Autonomous University of Barcelona
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作者：Dolgopyat, Dmitry; Dong, Changguang; Kanigowski, Adam; Nandori, Peter
作者单位：University System of Maryland; University of Maryland College Park; Yeshiva University; Nankai University; Nankai University
摘要：We exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: Zero entropy; Weak but not strong mixing; (Polynomial) mixing but not K; K but not Bernoulli and mixing at arbitrary fast polynomial rate. We also give an example of a system satisfying the CLT where the normalizing sequence is regularly varying with index 1. All these examples are C-infinity except for a zero entropy diffeomorphism satisfying the CLT whic...
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作者：Nicola, Fabio; Tilli, Paolo
作者单位：Polytechnic University of Turin
摘要：In this paper we solve an open problem concerning the characterization of those measurable sets Omega subset of R-2d that, among all sets having a prescribed Lebesgue measure, can trap the largest possible energy fraction in time-frequency space, where the energy density of a generic function f is an element of L-2(R-d) is defined in terms of its Short-time Fourier transform (STFT) nu f (x, omega), with Gaussian window. More precisely, given a measurable set Omega subset of R-2d having measure...
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作者：Xie, Junyi; Yuan, Xinyi
作者单位：Peking University
摘要：We give a proof of the full geometric Bogomolov conjecture.
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作者：Oh, Tadahiro; Sosoe, Philippe; Tolomeo, Leonardo
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; Cornell University; University of Bonn
摘要：We study an optimal mass threshold for normalizability of the Gibbs measures associated with the focusing mass-critical nonlinear Schrodinger equation on the one-dimensional torus. In an influential paper, Lebowitz et al. (J Stat Phys 50(3-4):657-687, 1988) proposed a critical mass threshold given by the mass of the ground state on the real line. We provide a proof for the optimality of this critical mass threshold. The proof also applies to the two-dimensional radial problem posed on the unit...
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作者：Disegni, Daniel
作者单位：Ben-Gurion University of the Negev
摘要：Let G be the group (GL(2) x GU(1))/GL(1) over a totally real field F, and let X be a Hida family for G. Revisiting a construction of Howard and Fouquet, we construct an explicit section P of a sheaf of Selmer groups over X. We show, answering a question of Howard, that P is a universal Heegner class, in the sense that it interpolates geometrically defined Heegner classes at all the relevant classical points of X. We also propose a 'Bertolini-Darmon' conjecture for the leading term of P at clas...
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作者：Berdnikov, Aleksandr; Manin, Fedor
作者单位：Institute for Advanced Study - USA; University of California System; University of California Santa Barbara
摘要：Scalable spaces are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are formal; indeed, scalability can be thought of as a metric version of formality. They are also characterized by particularly nice behavior from the point of view of quantitative homotopy theory. Among other results, we show that spaces which are formal but not scal...
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作者：Brue, Elia; Naber, Aaron; Semola, Daniele
作者单位：Institute for Advanced Study - USA; Northwestern University; University of Oxford
摘要：This paper studies the structure and stability of boundaries in noncollapsed RCD(K,N) spaces, that is, metric-measure spaces (X,d,H-N) with Ricci curvature bounded below. Our main structural result is that the boundary partial derivative X is homeomorphic to a manifold away from a set of codimension 2, and is N - 1 rectifiable. Along the way, we show effective measure bounds on the boundary and its tubular neighborhoods. These results are new even for Gromov-Hausdorff limits (M-i(N), d(gi), p(...
