2022

最新文章

• Diophantine approximation as Cosmic Censor for Kerr-AdS black holes AI翻译
  作者：Kehle, Christoph
  作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior of waves on black hole interiors with negative cosmological constant Lambda < 0 and explore the consequences of this for the Strong Cosmic Censorship conjecture in general relativity. We study linear scalar perturbations psi of Kerr-AdS solving square(g)psi - 2/3 Lambda psi = 0 with reflecting boundary conditions imposed at infinity. Understanding the behavior of psi at the Cauchy h...
• Geometry of 1-codimensional measures in Heisenberg groups AI翻译
  作者：Merlo, Andrea
  作者单位：Universite Paris Saclay
  摘要：This paper is devoted to the study of tangential properties of measures with density in the Heisenberg groups H-n. Among other results we prove that measures with (2n + 1)-density have only flat tangents and conclude the classification of uniform measures in H-1.
• The canonical wall structure and intrinsic mirror symmetry AI翻译
  作者：Gross, Mark; Siebert, Bernd
  作者单位：University of Cambridge; University of Texas System; University of Texas Austin
  摘要：As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015, Proceedings of Symposia in Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199-230, 2018) in 2016, we construct and prove consistency of the canonical wall structure. This construction starts with a log Calabi-Yau pair (X, D) and produces a wall structure, as defined in Gross et al. (Mem. Amer. Math. Soc. 278(1376), 1376, 1-103, 2022). Roughly put, the canonical wall structure is a data structure which encodes a...
• A homological approach to pseudoisotopy theory. I AI翻译
  作者：Krannich, Manuel
  作者单位：University of Cambridge
  摘要：We construct a zig-zag from the once delooped space of pseudoiso-topies of a closed 2n-disc to the once looped algebraic K -theory space of the integers and show that the maps involved are p-locally (2n - 4)-connected for n > 3 and large primes p. The proof uses the computation of the stable homology of the moduli space of high-dimensional handlebodies due to Botvinnik-Perlmutter and is independent of the classical approach to pseudoisotopy theory based on Igusa's stability theorem and work of...
• On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes AI翻译
  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...
• Characterising rectifiable metric spaces using tangent spaces AI翻译
  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...
• Representation growth and rational singularities of the moduli space of local systems (vol 204, pg 245, 2016) AI翻译
  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
• Flexibility of statistical properties for smooth systems satisfying the central limit theorem AI翻译
  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...
• The Faber-Krahn inequality for the short-time Fourier transform AI翻译
  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...
• Geometric Bogomolov conjecture in arbitrary characteristics AI翻译
  作者：Xie, Junyi; Yuan, Xinyi
  作者单位：Peking University
  摘要：We give a proof of the full geometric Bogomolov conjecture.