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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：Budzinski, Thomas; Curien, Nicolas; Petri, Bram
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Universite Paris Saclay; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France
摘要：It is a well-known result due to Bollob & aacute;s that the maximal Cheeger constant of large d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d$\end{document}-regular graphs cannot be close to the Cheeger constant of the d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} ...
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作者：Guichard, Olivier; Wienhard, Anna
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Max Planck Society
摘要：We introduce the notion of Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Theta $\end{document}-positivity in real semisimple Lie groups. This notion at the same time generalizes Lusztig's total positivity in split real Lie groups and invariant orders in Lie groups of Hermitian type. We show that there are fo...
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作者：Osajda, Damian; Przytycki, Piotr
作者单位：University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; McGill University
摘要：We prove that Coxeter groups are biautomatic. From our construction of the biautomatic structure it follows that uniform lattices in isometry groups of buildings are biautomatic.
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作者：Lim, Willie Rush
作者单位：Brown University
摘要：By adapting the near-degenerate regime designed by Kahn, Lyubich, and D. Dudko, we prove that the boundaries of Herman rings with bounded type rotation number and of the simplest configuration are quasicircles with dilatation depending only on the degree and the rotation number. As a consequence, we show that these Herman rings always degenerate to a Herman curve, i.e. an invariant Jordan curve that is not contained in the closure of a rotation domain and on which the map is conjugate to a rig...
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作者：Li, Yangyang; Wang, Zhihan
作者单位：University of Chicago
摘要：We show that in an 8-dimensional closed Riemmanian manifold with Cam-generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic regularity conjecture of minimal hypersurfaces in dimension eight. This also enables us to generalize many generic geometric properties of (Almgren-Pitts) min-max minimal hypersurfaces, previously only known in low dimensions, to dimension eight. En route to our main results, we have proved a sheeting theorem for minimal hype...
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作者：Even-Zohar, Chaim; Lakrec, Tsviqa; Tessler, Ran J.
作者单位：Technion Israel Institute of Technology; University of Zurich; Weizmann Institute of Science
摘要：The amplituhedron An,k,4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A}_{n,k,4}$\end{document} is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that An,k,4\documentclass[12pt]{minimal} \usepackage{amsmath} ...
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作者：Maulik, Davesh; Shen, Junliang; Yin, Qizheng; Zhang, Ruxuan
作者单位：Massachusetts Institute of Technology (MIT); Yale University; Peking University; Fudan University
摘要：We show that birational hyper-K & auml;hler varieties of K3[n]-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-K & auml;hler varieties of K3[n]-type with Brauer classes.
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作者：Martin, Daniel E.
作者单位：Clemson University
摘要：In 2021, Chen proved that the size of any connected component of the Markoff mod p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p$\end{document} graph is divisible by p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...
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作者：Arone, Gregory; Barthel, Tobias; Heard, Drew; Sanders, Beren
作者单位：Stockholm University; Max Planck Society; Norwegian University of Science & Technology (NTNU); University of California System; University of California Santa Cruz
摘要：We prove a thick subcategory theorem for the category of d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d$\end{document}-excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the d=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \us...
