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On curves in K-theory and TR 关于k理论和TR中的曲线
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-16 DOI: 10.4171/jems/1347
Jonas McCandless
{"title":"On curves in K-theory and TR","authors":"Jonas McCandless","doi":"10.4171/jems/1347","DOIUrl":"https://doi.org/10.4171/jems/1347","url":null,"abstract":"We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line $mathbf{S}[t]$ as a functor defined on the $infty$-category of cyclotomic spectra with values in the $infty$-category of spectra with Frobenius lifts, refining a result of Blumberg-Mandell. We define the notion of an integral topological Cartier module using Barwick's formalism of spectral Mackey functors on orbital $infty$-categories, extending the work of Antieau-Nikolaus in the $p$-typical setting. As an application, we show that TR evaluated on a connective $mathbf{E}_1$-ring admits a description in terms of the spectrum of curves on algebraic K-theory generalizing the work of Hesselholt and Betley-Schlichtkrull.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82381844","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
Cutoff for non-negatively curved Markov chains 非负弯曲马尔可夫链的截断
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-10 DOI: 10.4171/jems/1348
J. Salez
{"title":"Cutoff for non-negatively curved Markov chains","authors":"J. Salez","doi":"10.4171/jems/1348","DOIUrl":"https://doi.org/10.4171/jems/1348","url":null,"abstract":"Discovered in the context of card shuffling by Aldous, Diaconis and Shahshahani, the cutoff phenomenon has since then been established in a variety of Markov chains. However, proving cutoff remains a delicate affair, which requires a detailed knowledge of the chain. Identifying the general mechanisms underlying this phase transition -- without having to pinpoint its precise location -- remains one of the most fundamental open problems in the area of mixing times. In the present paper, we make a step in this direction by establishing cutoff for Markov chains with non-negative curvature, under a suitably refined product condition. The result applies, in particular, to random walks on abelian Cayley expanders satisfying a mild degree condition, hence in particular to emph{almost all} abelian Cayley graphs. Our proof relies on a quantitative emph{entropic concentration principle}, which we believe to lie behind all cutoff phenomena.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87782281","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: 20
PFH spectral invariants on the two-sphere and the large scale geometry of Hofer’s metric 双球上的PFH谱不变量及Hofer度规的大尺度几何
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-08 DOI: 10.4171/jems/1351
Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini
{"title":"PFH spectral invariants on the two-sphere and the large scale geometry of Hofer’s metric","authors":"Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini","doi":"10.4171/jems/1351","DOIUrl":"https://doi.org/10.4171/jems/1351","url":null,"abstract":"We resolve three longstanding questions related to the large scale geometry of the group of Hamiltonian diffeomorphisms of the two-sphere, equipped with Hofer's metric. Namely: (1) we resolve the Kapovich-Polterovich question by showing that this group is not quasi-isometric to the real line; (2) more generally, we show that the kernel of Calabi over any proper open subset is unbounded; and (3) we show that the group of area and orientation preserving homeomorphisms of the two-sphere is not a simple group. We also obtain, as a corollary, that the group of area-preserving diffeomorphisms of the open disc, equipped with an area-form of finite area, is not perfect. Central to all of our proofs are new sequences of spectral invariants over the two-sphere, defined via periodic Floer homology.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74088723","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: 12
A quantization proof of the uniform Yau–Tian–Donaldson conjecture 统一you - tian - donaldson猜想的量化证明
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-04 DOI: 10.4171/jems/1373
Kewei Zhang
{"title":"A quantization proof of the uniform Yau–Tian–Donaldson conjecture","authors":"Kewei Zhang","doi":"10.4171/jems/1373","DOIUrl":"https://doi.org/10.4171/jems/1373","url":null,"abstract":"Using quantization techniques, we show that the $delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence of twisted K\"ahler-Einstein metrics with arbitrary polarizations. Our approach mainly uses pluripotential theory, which does not involve Cheeger-Colding-Tian theory or the non-Archimedean language. A new computable criterion for the existence of constant scalar curvature K\"ahler metrics is also given.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77777085","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: 21
Bounds for twists of GL(3) $L$-functions GL(3) $L$-函数的扭转边界
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-03 DOI: 10.4171/JEMS/1046
Yongxiao Lin
{"title":"Bounds for twists of GL(3) $L$-functions","authors":"Yongxiao Lin","doi":"10.4171/JEMS/1046","DOIUrl":"https://doi.org/10.4171/JEMS/1046","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82957522","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: 17
Erratum to “Harmonic Maass forms associated to real quadratic fields” “与实二次场相关的调和质量形式”的勘误
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-02-02 DOI: 10.4171/JEMS/1043
Pierre Charollois, Yingkun Li
{"title":"Erratum to “Harmonic Maass forms associated to real quadratic fields”","authors":"Pierre Charollois, Yingkun Li","doi":"10.4171/JEMS/1043","DOIUrl":"https://doi.org/10.4171/JEMS/1043","url":null,"abstract":"[1] Pierre Charollois, Yingkun Li, Harmonic Maass forms associated to real quadratic fields, JEMS 22, 1115–1148 (2020). [2] Yingkun Li, Markus Schwagenscheidt, Mock modular forms with integral Fourier coefficients, preprint, arxiv:2101.05583 (2021). [3] Nils Scheithauer, The Weil Representation of SL2(Z) and Some Applications, Int. Math. Res. Not., no. 8, 1488–1545 (2009). E-mail address: pierre.charollois@imj-prg.fr E-mail address: li@mathematik.tu-darmstadt.de","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75686511","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
Kernels of conditional determinantal measures and the Lyons–Peres completeness conjecture
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-19 DOI: 10.4171/JEMS/1038
A. Bufetov, Yanqi Qiu, A. Shamov
{"title":"Kernels of conditional determinantal measures and the Lyons–Peres completeness conjecture","authors":"A. Bufetov, Yanqi Qiu, A. Shamov","doi":"10.4171/JEMS/1038","DOIUrl":"https://doi.org/10.4171/JEMS/1038","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72480122","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: 9
On geometrically finite degenerations I: boundaries of main hyperbolic components 几何有限退化I:主要双曲分量的边界
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-19 DOI: 10.4171/jems/1342
Yusheng Luo
{"title":"On geometrically finite degenerations I: boundaries of main hyperbolic components","authors":"Yusheng Luo","doi":"10.4171/jems/1342","DOIUrl":"https://doi.org/10.4171/jems/1342","url":null,"abstract":"In this paper, we develop a theory on the degenerations of Blaschke products $mathcal{B}_d$ to study the boundaries of hyperbolic components. We give a combinatorial classification of geometrically finite polynomials on the boundary of the main hyperbolic component $mathcal{H}_d$ containing $z^d$. We show the closure $overline{mathcal{H}_d}$ is not a topological manifold with boundary for $dgeq 4$ by constructing self-bumps on its boundary.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74055930","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: 4
Hermitian operators and isometries on symmetric operator spaces 对称算子空间上的厄米算子和等距
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-11 DOI: 10.4171/jems/1332
Jinghao Huang, F. Sukochev
{"title":"Hermitian operators and isometries on symmetric operator spaces","authors":"Jinghao Huang, F. Sukochev","doi":"10.4171/jems/1332","DOIUrl":"https://doi.org/10.4171/jems/1332","url":null,"abstract":"Let $mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal trace $tau$. Let $E(mathcal{M},tau) $ be a symmetric operator space affiliated with $ mathcal{M} $, whose norm is order continuous and is not proportional to the Hilbertian norm $left|cdotright|_2$ on $L_2(mathcal{M},tau)$. We obtain general description of all bounded hermitian operators on $E(mathcal{M},tau)$. This is the first time that the description of hermitian operators on asymmetric operator space (even for a noncommutative $L_p$-space) is obtained in the setting of general (non-hyperfinite) von Neumann algebras. As an application, we resolve a long-standing open problem concerning the description of isometries raised in the 1980s, which generalizes and unifies numerous earlier results.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87245097","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
A subspace theorem for manifolds 流形的子空间定理
IF 2.6 1区 数学
Journal of the European Mathematical Society Pub Date : 2021-01-11 DOI: 10.4171/jems/1346
E. Breuillard, Nicolas de Saxc'e
{"title":"A subspace theorem for manifolds","authors":"E. Breuillard, Nicolas de Saxc'e","doi":"10.4171/jems/1346","DOIUrl":"https://doi.org/10.4171/jems/1346","url":null,"abstract":"We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope formalism and the corresponding notion of semistability for diagonal flows.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82648267","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
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