Inventiones mathematicae

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• Product structure and regularity theorem for totally nonnegative flag varieties AI翻译
  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...
• Virasoro constraints for moduli of sheaves and vertex algebras AI翻译
  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...
• A prismatic approach to crystalline local systems AI翻译
  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...
• SRB measures for C∞ surface diffeomorphisms AI翻译
  作者：Burguet, David
  作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：AC(infinity) smooth surface diffeomorphism admits an SRB measure if and only if the set{x,lim sup(n)(1)/(n )log & Vert;d(x)f(n)& Vert;>0}has positive Lebesgue measure. Moreover the basinsof the ergodic SRB measures are covering this set Lebesgue almost everywhere. Wealso obtain similar results forCrsurface diffeomorphisms with+infinity>r>1.
• Higher Siegel-Weil formula for unitary groups: the non-singular terms AI翻译
  作者：Feng, Tony; Yun, Zhiwei; Zhang, Wei
  作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
  摘要：We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the rth central derivative of non-singular Fourier coefficients of a normalized Siegel-Eisenstein series, and (2) the degree of special cycles of virtual dimension 0 on the moduli stack of hermitian shtukas with r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein seri...
• The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions AI翻译
  作者：Shkoller, Steve; Vicol, Vlad
  作者单位：University of California System; University of California Davis; New York University
  摘要：We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which is necessary for the local shock development problem. For an open set of compressive and generic H7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{...
• A p-adic arithmetic inner product formula AI翻译
  作者：Disegni, Daniel; Liu, Yifeng
  作者单位：Ben-Gurion University of the Negev; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Zhejiang University
  摘要：Fix a prime number p and let E/F be a CM extension of number fields in which p splits relatively. Let pi be an automorphic representation of a quasi-split unitary group of even rank with respect to E/F such that pi is ordinary above p with respect to the Siegel parabolic subgroup. We construct the cyclotomic p-adic L-function of pi, and a certain generating series of Selmer classes of special cycles on Shimura varieties. We show, under some conditions, that if the vanishing order of the p-adic...
• Quantitative bounds in the nonlinear Roth theorem AI翻译
  作者：Peluse, Sarah; Prendiville, Sean
  作者单位：Stanford University; Lancaster University
  摘要：We show that there exists c>0 such that any subset of {1, ... ,N} of density at least (log log N)(-c) contains a nontrivial progression of the form x, x+y, x+y(2). This is the first quantitatively effective version of the Bergelson-Leibman polynomial Szemeredi theorem for a progression involving polynomials of differing degrees. Our key innovation is an inverse theorem characterising sets for which the number of configurations x, x+y, x+y(2) deviates substantially from the expected value. In p...
• Hamiltonian Floer theory on surfaces: linking, positively transverse foliations and spectral invariants AI翻译
  作者：Connery-Grigg, Dustin
  作者单位：Sorbonne Universite
  摘要：We develop connections between the qualitative dynamics of Hamiltonian isotopies on a surface Sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Sigma $\end{document} and their chain-level Floer theory using ideas drawn from Hofer-Wysocki-Zehnder's theory of finite energy foliations. We associate to every collect...
• Uniform negative immersions and the coherence of one-relator groups AI翻译
  作者：Louder, Larsen; Wilton, Henry
  作者单位：University of London; University College London; University of Cambridge
  摘要：Previously, the authors proved that the presentation complex of a one-relator group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepack...