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Infinite volume and infinite injectivity radius 无限体积和无限注入半径
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-03 DOI: 10.4007/annals.2023.197.1.6
Mikolaj Fraczyk, T. Gelander
{"title":"Infinite volume and infinite injectivity radius","authors":"Mikolaj Fraczyk, T. Gelander","doi":"10.4007/annals.2023.197.1.6","DOIUrl":"https://doi.org/10.4007/annals.2023.197.1.6","url":null,"abstract":"We prove the following conjecture of Margulis. Let G be a higher rank simple Lie group and let Λ ≤ G be a discrete subgroup of infinite covolume. Then, the locally symmetric space ΛG/K admits injected balls of any radius. This can be considered as a geometric interpretation of the celebrated Margulis normal subgroup theorem. However, it applies to general discrete subgroups not necessarily associated to lattices. Yet, the result is new even for subgroups of infinite index of lattices. We establish similar results for higher rank semisimple groups with Kazhdan’s property (T). We prove a stiffness result for discrete stationary random subgroups in higher rank semisimple groups and a stationary variant of the Stück–Zimmer theorem for higher rank semisimple groups with property (T). We also show that a stationary limit of a measure supported on discrete subgroups is almost surely discrete.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43796068","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
Integer multiplication in time O(n log n) O(n log n)时间内的整数乘法
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/ANNALS.2021.193.2.4
David Harvey, J. Hoeven
{"title":"Integer multiplication in time O(n log n)","authors":"David Harvey, J. Hoeven","doi":"10.4007/ANNALS.2021.193.2.4","DOIUrl":"https://doi.org/10.4007/ANNALS.2021.193.2.4","url":null,"abstract":"We present an algorithm that computes the product of two n-bit integers in O(n log n) bit operations, thus confirming a conjecture of Schonhage and Strassen from 1971. Our complexity analysis takes place in the multitape Turing machine model, with integers encoded in the usual binary representa- tion. Central to the new algorithm is a novel “Gaussian resampling” technique that enables us to reduce the integer multiplication problem to a collection of multidimensional discrete Fourier transforms over the complex numbers, whose dimensions are all powers of two. These transforms may then be evaluated rapidly by means of Nussbaumer’s fast polynomial transforms.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186827","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: 164
Coefficients of Maass Forms and the Siegel Zero 质量形式系数和西格尔零
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.2307/2118543
Jeffrey Hoffstein And Paul Lockhart
{"title":"Coefficients of Maass Forms and the Siegel Zero","authors":"Jeffrey Hoffstein And Paul Lockhart","doi":"10.2307/2118543","DOIUrl":"https://doi.org/10.2307/2118543","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2307/2118543","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69188289","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: 91
Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below Ricci曲率下有界的非坍缩极限空间奇异集的可整流性
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/ANNALS.2021.193.2.2
J. Cheeger, Wenshuai Jiang, A. Naber
{"title":"Rectifiability of singular sets of noncollapsed limit spaces with\u0000 Ricci curvature bounded below","authors":"J. Cheeger, Wenshuai Jiang, A. Naber","doi":"10.4007/ANNALS.2021.193.2.2","DOIUrl":"https://doi.org/10.4007/ANNALS.2021.193.2.2","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"193 1","pages":"407-538"},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186320","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: 34
The threshold conjecture for the energy critical hyperbolic Yang–Mills equation 能量临界双曲Yang-Mills方程的阈值猜想
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.194.2.1
Oh, Tataru
{"title":"The threshold conjecture for the energy critical hyperbolic\u0000 Yang–Mills equation","authors":"Oh, Tataru","doi":"10.4007/annals.2021.194.2.1","DOIUrl":"https://doi.org/10.4007/annals.2021.194.2.1","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186889","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
Martin's Maximum++ implies Woodin's axiom (*) 马丁最大值++暗含伍丁公理(*)
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/ANNALS.2021.193.3.3
D. Asperó, R. Schindler
{"title":"Martin's Maximum++ implies Woodin's axiom\u0000 (*)","authors":"D. Asperó, R. Schindler","doi":"10.4007/ANNALS.2021.193.3.3","DOIUrl":"https://doi.org/10.4007/ANNALS.2021.193.3.3","url":null,"abstract":"We show that Martin’s Maximum++ implies Woodin’s Pmax axiom (∗). This answers a question from the 1990’s and amalgamates two prominent axioms of set theory which were both known to imply that there are א2 many real numbers.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"193 1","pages":"793-835"},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186839","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: 22
On property (T) for Aut(Fn) and SLn(ℤ) 关于Aut(Fn)和SLn(n)的性质(T)
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.193.2.3
Kaluba, Kielak, Nowak
{"title":"On property (T) for Aut(<em>F<sub>n</sub></em>) and\u0000 SL<sub><em>n</em></sub>(ℤ)","authors":"Kaluba, Kielak, Nowak","doi":"10.4007/annals.2021.193.2.3","DOIUrl":"https://doi.org/10.4007/annals.2021.193.2.3","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186504","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
Strong generators in Dperf(X) and Dbcoh(X) Dperf(X)和Dbcoh(X)中的强生成器
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.193.3.1
Neeman
{"title":"Strong generators in D<sup>perf</sup>(<em>X</em>) and\u0000 D<em><sup>b</sup></em><sub>coh</sub>(<em>X</em>)","authors":"Neeman","doi":"10.4007/annals.2021.193.3.1","DOIUrl":"https://doi.org/10.4007/annals.2021.193.3.1","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186752","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
Index 指数
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.193.3.0979
{"title":"Index","authors":"","doi":"10.4007/annals.2021.193.3.0979","DOIUrl":"https://doi.org/10.4007/annals.2021.193.3.0979","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186925","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 non-hypergeometric $E$-function 一个非超几何的E函数
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-12-20 DOI: 10.4007/annals.2021.194.3.7
J. Fres'an, P. Jossen
{"title":"A non-hypergeometric $E$-function","authors":"J. Fres'an, P. Jossen","doi":"10.4007/annals.2021.194.3.7","DOIUrl":"https://doi.org/10.4007/annals.2021.194.3.7","url":null,"abstract":"We answer in the negative Siegel’s question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential operator of order three annihilates an E-function in the hypergeometric class, then the singularities of its Fourier transform are constrained to satisfy a symmetry property that generically does not hold. The proof relies on André’s theory of E-operators and Katz’s computation of the Galois group of hypergeometric differential equations.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2020-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44995606","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
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