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作者：Wang, Hong; Zahl, Joshua
作者单位：New York University; University of British Columbia
摘要：This paper studies the structure of Kakeya sets in R-3. We show that for every Kakeya set K subset of R-3, there exist well-separated scales 0 < delta < rho <= 1 so that the delta neighborhood of K is almost as large as the rho neighborhood of K. As a consequence, every Kakeya set in R-3 has Assouad dimension 3 and every Ahlfors-David regular Kakeya set in R-3 has Hausdorff dimension 3. We also show that every Kakeya set in R-3 that has stably equal Hausdorff and packing dimension (this is a n...
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作者：Alon, Lior; Kummer, Mario; Kurasov, Pavel; Vinzant, Cynthia
作者单位：Massachusetts Institute of Technology (MIT); Technische Universitat Dresden; Stockholm University; University of Washington; University of Washington Seattle
摘要：In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb{C}}<^>...
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作者：Chen, Shibing; Liu, Jiakun
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Sydney
摘要：In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not exhibit any form of convexity a priori, we prove its higher order regularity by developing novel methods, which also have many other applications. Notably, our results are achieved without requiring any convexity of the source domain. This aligns with Caffarell...
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作者：Walsh, Miguel N.
作者单位：University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of Buenos Aires
摘要：We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least (logX)psi(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\log X)<^>{\psi (X)}$\end{document}, with psi(X)->infinit...
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作者：Donvil, Milan; Vaes, Stefaan
作者单位：KU Leuven
摘要：We construct countable groups G with the following new degree of W*-superrigidity: if L(G) is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra L(Lambda), then the groups G and Lambda must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary 2-cocycle. We also give examples of II1 factors N that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twis...
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作者：Dong, Conghan; Song, Antoine
作者单位：State University of New York (SUNY) System; Stony Brook University; California Institute of Technology
摘要：We show that the Euclidean 3-space R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}<^>{3}$\end{document} is stable for the Positive Mass Theorem in the following sense. Let (Mi,gi)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackag...
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作者：Spaeth, Britta
作者单位：University of Wuppertal
摘要：We determine the action of the automorphism group Aut(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm {Aut}(G)$\end{document} on the set of irreducible characters Irr(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us...
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作者：Marrakchi, Amine
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：In 1967, Kadison asked if N is a subfactor of the factor M for which N 'boolean AND Mconsistsof scalars, will some maximal abelian *-subalgebra of Nbe a maximal abelian sub-algebra of M?. Generalizing a theorem of Popa in the type II case (1981), we solve Kadison's problem for all subfactors with expectation N subset of M where Nis either atype III lambda factor with 0 <=lambda<1 or a type III 1 factor that satisfies Connes's bicentralizer conjecture. Our solution is based on a new explicit fo...
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作者：Maulik, Davesh; Shen, Junliang; Yin, Qizheng; Zhang, Ruxuan
作者单位：Massachusetts Institute of Technology (MIT); Yale University; Peking University; Fudan University
摘要：We show that birational hyper-K & auml;hler varieties of K3[n]-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-K & auml;hler varieties of K3[n]-type with Brauer classes.
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作者：Heuer, Ben
作者单位：Goethe University Frankfurt
摘要：For any smooth proper rigid analytic space X over a complete algebraically closed extension of Qp, we construct a p-adic Simpson correspondence: an equivalence of categories between vector bundles on Scholze's pro-etale site of X and Higgs bundles on X. This generalises a result of Faltings from smooth projective curves to any higher dimension, and further to the rigid analytic setup. The strategy is new, and is based on the study of rigid analytic moduli spaces of pro-etale invertible sheaves...
