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Outer space for RAAGs 为RAAGs提供外太空
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-07-19 DOI: 10.1215/00127094-2023-0007
Corey Bregman, Ruth Charney, K. Vogtmann
{"title":"Outer space for RAAGs","authors":"Corey Bregman, Ruth Charney, K. Vogtmann","doi":"10.1215/00127094-2023-0007","DOIUrl":"https://doi.org/10.1215/00127094-2023-0007","url":null,"abstract":"For any right-angled Artin group $A_{Gamma}$ we construct a finite-dimensional space $mathcal{O}_{Gamma}$ on which the group $text{Out}(A_{Gamma})$ of outer automorphisms of $A_{Gamma}$ acts properly. We prove that $mathcal{O}_{Gamma}$ is contractible, so that the quotient is a rational classifying space for $text{Out}(A_{Gamma})$. The space $mathcal{O}_{Gamma}$ blends features of the symmetric space of lattices in $mathbb{R}^n$ with those of Outer space for the free group $F_n$. Points in $mathcal{O}_{Gamma}$ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with $A_{Gamma}$.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43758456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Prime numbers in two bases 两进制的质数
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-07-15 DOI: 10.1215/00127094-2019-0083
M. Drmota, C. Mauduit, J. Rivat
{"title":"Prime numbers in two bases","authors":"M. Drmota, C. Mauduit, J. Rivat","doi":"10.1215/00127094-2019-0083","DOIUrl":"https://doi.org/10.1215/00127094-2019-0083","url":null,"abstract":"If q1 and q2 are two coprime bases, f (resp. g) a strongly q1-multiplicative (resp. strongly q2-multiplicative) function of modulus 1 and θ a real number, we estimate the sums ∑ n≤x Λ(n)f(n)g(n) exp(2iπθn) (and ∑ n≤x μ(n)f(n)g(n) exp(2iπθn)), where Λ denotes the von Mangoldt function (and μ the Möbius function). The goal of this work is to introduce a new approach to study these sums involving simultaneously two different bases combining Fourier analysis, Diophantine approximation and combinatorial arguments. We deduce from these estimates a Prime Number Theorem (and Möbius orthogonality) for sequences of integers with digit properties in two coprime bases.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47289272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Convexity estimates for hypersurfaces moving by concave curvature functions 由凹曲率函数移动的超曲面的凸性估计
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-07-15 DOI: 10.1215/00127094-2022-0011
S. Lynch
{"title":"Convexity estimates for hypersurfaces moving by concave curvature functions","authors":"S. Lynch","doi":"10.1215/00127094-2022-0011","DOIUrl":"https://doi.org/10.1215/00127094-2022-0011","url":null,"abstract":"We study fully nonlinear geometric flows that deform strictly $k$-convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of the principal curvatures. Specifically, the speeds we consider are obtained by performing a nonlinear interpolation between the mean and the $k$-harmonic mean of the principal curvatures. Our main result is a convexity estimate showing that, on compact solutions, regions of high curvature are approximately convex. In contrast to the mean curvature flow, the fully nonlinear flows considered here preserve $k$-convexity in a Riemannian background, and we show that the convexity estimate carries over to this setting as long as the ambient curvature satisfies a natural pinching condition.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42043778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Real and symmetric matrices 实矩阵和对称矩阵
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-06-18 DOI: 10.1215/00127094-2022-0076
Tsao-Hsien Chen, D. Nadler
{"title":"Real and symmetric matrices","authors":"Tsao-Hsien Chen, D. Nadler","doi":"10.1215/00127094-2022-0076","DOIUrl":"https://doi.org/10.1215/00127094-2022-0076","url":null,"abstract":"We construct a stratified homeomorphism between the space of $ntimes n$ real matrices with real eigenvalues and the space of $ntimes n$ symmetric matrices with real eigenvalues, which restricts to a real analytic isomorphism between individual $GL_n(mathbb R)$-adjoint orbits and $O_n(mathbb C)$-adjoint orbits. We also establish similar results in more general settings of Lie algebras of classical types and quiver varieties. To this end, we prove a general result about involutions on hyper-Kahler quotients of linear spaces. We discuss applications to the (generalized) Kostant-Sekiguchi correspondence, singularities of real and symmetric adjoint orbit closures, and Springer theory for real groups and symmetric spaces.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46569461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher coherent cohomology and p -adic modular forms of singular weights 高相干上同调与奇异权的p-adic模形式
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-06-15 DOI: 10.1215/00127094-2019-0075
V. Pilloni
{"title":"Higher coherent cohomology and p -adic modular forms of singular weights","authors":"V. Pilloni","doi":"10.1215/00127094-2019-0075","DOIUrl":"https://doi.org/10.1215/00127094-2019-0075","url":null,"abstract":"— We investigate the p-adic properties of higher coherent cohomology of automorphic vector bundles of singular weights on the Siegel threefolds. 2000 Mathematics Subject Classification: 11F33, 11G18, 14G35","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48500603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
Gradient variational problems in R2 R2中的梯度变分问题
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-06-01 DOI: 10.1215/00127094-2022-0036
R. Kenyon, I. Prause
{"title":"Gradient variational problems in R2","authors":"R. Kenyon, I. Prause","doi":"10.1215/00127094-2022-0036","DOIUrl":"https://doi.org/10.1215/00127094-2022-0036","url":null,"abstract":"We prove a new integrability principle for gradient variational problems in $mathbb{R}^2$, showing that solutions are explicitly parameterized by $kappa$-harmonic functions, that is, functions which are harmonic for the laplacian with varying conductivity $kappa$, where $kappa$ is the square root of the Hessian determinant of the surface tension.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47543479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Upper bounds on number fields of given degree and bounded discriminant 给定次数数域的上界与有界判别式
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-28 DOI: 10.1215/00127094-2022-0046
R. Oliver, F. Thorne
{"title":"Upper bounds on number fields of given degree and bounded discriminant","authors":"R. Oliver, F. Thorne","doi":"10.1215/00127094-2022-0046","DOIUrl":"https://doi.org/10.1215/00127094-2022-0046","url":null,"abstract":"Let $N_n(X)$ denote the number of degree $n$ number fields with discriminant bounded by $X$. In this note, we improve the best known upper bounds on $N_n(X)$, finding that $N_n(X) = O(X^{ c (log n)^2})$ for an explicit constant $c$.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46491984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 36
Poincaré series and linking of Legendrian knots Poincaré 系列和 Legendrian 节的连接
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-26 DOI: 10.1215/00127094-2023-0008
Nguyen Viet Dang IMJ-PRG, Iuf, Gabriel Rivière
{"title":"Poincaré series and linking of Legendrian knots","authors":"Nguyen Viet Dang IMJ-PRG, Iuf, Gabriel Rivière","doi":"10.1215/00127094-2023-0008","DOIUrl":"https://doi.org/10.1215/00127094-2023-0008","url":null,"abstract":"On a negatively curved surface, we show that the Poincare series counting geodesic arcs orthogonal to some pair of closed geodesic curves has a meromorphic continuation to the whole complex plane. When both curves are homologically trivial, we prove that the Poincare series has an explicit rational value at 0 interpreting it in terms of linking number of Legendrian knots. In particular, for any pair of points on the surface, the lengths of all geodesic arcs connecting the two points determine its genus, and, for any pair of homologically trivial closed geodesics, the lengths of all geodesic arcs orthogonal to both geodesics determine the linking number of the two geodesics.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141202811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Diagonal Ramsey via effective quasirandomness 对角线拉姆齐通过有效的准随机
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-19 DOI: 10.1215/00127094-2022-0048
A. Sah
{"title":"Diagonal Ramsey via effective quasirandomness","authors":"A. Sah","doi":"10.1215/00127094-2022-0048","DOIUrl":"https://doi.org/10.1215/00127094-2022-0048","url":null,"abstract":"We improve the upper bound for diagonal Ramsey numbers to [R(k+1,k+1)leexp(-c(log k)^2)binom{2k}{k}] for $kge 3$. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal \"effective quasirandomness\" results about convergence of graphs. This optimality represents a natural barrier to improvement.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47237326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 36
Galois action on universal covers of Kodaira fibrations 对Kodaira纤维的通用盖的伽罗瓦作用
IF 2.5 1区 数学
Duke Mathematical Journal Pub Date : 2020-05-15 DOI: 10.1215/00127094-2019-0078
G. González‐diez
{"title":"Galois action on universal covers of Kodaira fibrations","authors":"G. González‐diez","doi":"10.1215/00127094-2019-0078","DOIUrl":"https://doi.org/10.1215/00127094-2019-0078","url":null,"abstract":"F. Catanese has recently asked if there exists an element of the absolute Galois group σ ∈ Gal(Q) for which there is a Kodaira fibration f : S → B defined over a number field such that the universal covers of S and its Galois conjugate surface S are not isomorphic. The main result of this article is that every element σ 6= Id. has this property.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48659962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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