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作者：Huang, Jingyin
作者单位：University System of Ohio; Ohio State University
摘要：We show that for a large class of Artin groups with Dynkin diagrams being a tree, the K(pi,1)-conjecture holds. We also establish the K(pi,1)-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which applies to some hyperbolic type Artin groups. This is based on a new approach to the K(pi,1)-conjecture for Artin groups.
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作者：De Roeck, Wojciech; Elgart, Alexander; Fraas, Martin
作者单位：KU Leuven; Virginia Polytechnic Institute & State University
摘要：This work justifies the linear response formula for the Hall conductance of a two-dimensional disordered system. The proof rests on controlling the dynamics associated with a random time-dependent Hamiltonian. The principal challenge is related to the fact that spectral and dynamical localization are intrinsically unstable under perturbation, and the exact spectral flow - the tool used previously to control the dynamics in this context - does not exist. We resolve this problem by proving a loc...
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作者：Ji, Ran; Wu, Yunhui
作者单位：Tsinghua University; Capital Normal University; Tsinghua University
摘要：In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document} of finite volume with sectional curvature -1 <= K <= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
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作者：Karpukhin, Mikhail; Stern, Daniel
作者单位：California Institute of Technology; University of Chicago
摘要：We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold (M-n,g) of dimension n>2 to any closed, non-aspherical manifold N containing no stable minimal two-spheres. In particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special case of the round spheres N=S-k, k >= 3, we obtain a distinguished family of nonconstant harmonic maps M ->...
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作者：Killip, Rowan; Laurens, Thierry; Visan, Monica
作者单位：University of California System; University of California Los Angeles; University of Wisconsin System; University of Wisconsin Madison
摘要：The Benjamin-Ono equation is shown to be well-posed, both on the line and on the circle, in the Sobolev spaces H(s )for s>-(1)|(2). The proof rests on a new gauge transfor-mation and benefits from our introduction of a modified Lax pair representation of the full hierarchy. As we will show, these developments yield important additional divi-dends beyond well-posedness, including (i) the unification of the diverse approaches to polynomial conservation laws; (ii) a generalization of G & eacute;r...
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作者：Baldi, Gregorio; Klingler, Bruno; Ullmo, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Humboldt University of Berlin
摘要：Given a polarizable Z-variation of Hodge structures V over a complex smooth quasi-projective base S, a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional Hodge tensors appear) is a countable union of irreducible algebraic subvarieties of S, called the special subvarieties for V. Our main result in this paper is that, if the level of V is at least 3, this Hodge locus is in fact a finite union of such special subvarieties (hence is algebra...
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作者：Sawin, Will; Wood, Melanie Matchett
作者单位：Princeton University; Harvard University
摘要：For G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} and H1,& mldr;,Hn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H...
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作者：Bao, Huanchen; He, Xuhua
作者单位：National University of Singapore; University of Hong Kong
摘要：The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) J \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$J$\end{document} -total positivity on the full flag variety of an arbitrary Kac-Moody group, ge...
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作者：Bojko, Arkadij; Lim, Woonam; Moreira, Miguel
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf theoretic Virasoro constraints in terms of primary states coming from a natural conformal vector in Joyce's vertex algebra. This shows that Virasoro constraints are preserved under wall-crossing. As an application, we prove the conjectural Virasoro constraints for moduli spaces of torsion-free sheaves...
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作者：Guo, Haoyang; Reinecke, Emanuel
作者单位：University of Chicago; Institute for Advanced Study - USA
摘要：Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} be a smooth p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p$\en...
