Pub Date : 2023-12-29DOI: 10.4007/annals.2024.199.1.8
Gregorio Baldi, Emmanuel Ullmo
No abstract available for this article
本文无摘要
{"title":"Erratum to “Special subvarieties of non-arithmetic ball quotients and Hodge theory” | Annals of Mathematics","authors":"Gregorio Baldi, Emmanuel Ullmo","doi":"10.4007/annals.2024.199.1.8","DOIUrl":"https://doi.org/10.4007/annals.2024.199.1.8","url":null,"abstract":"<h3>No abstract available for this article</h3>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"13 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064128","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}
Pub Date : 2023-12-29DOI: 10.4007/annals.2024.199.1.1
Oded Regev, Noah Stephens-Davidowitz
We prove a conjecture due to Dadush, showing that if $mathcal{L} subset mathbb{R}^n$ is a lattice such that $mathrm{det}(mathcal{L}’)ge 1$ for all sublattices $mathcal{L}’ subseteq mathcal{L}$, then $sum_{mathbf{y}in mathcal{L}} e^{-pi t^2 |mathbf{y} |^2} le 3/2$, where $t := 10(log n + 2)$. From this we derive bounds on the number of short lattice vectors, which can be viewed as a partial converse to Minkowski’s celebrated first theorem. We also derive a bound on the covering radius.
{"title":"A reverse Minkowski theorem | Annals of Mathematics","authors":"Oded Regev, Noah Stephens-Davidowitz","doi":"10.4007/annals.2024.199.1.1","DOIUrl":"https://doi.org/10.4007/annals.2024.199.1.1","url":null,"abstract":"<p>We prove a conjecture due to Dadush, showing that if $mathcal{L} subset mathbb{R}^n$ is a lattice such that $mathrm{det}(mathcal{L}’)ge 1$ for all sublattices $mathcal{L}’ subseteq mathcal{L}$, then $sum_{mathbf{y}in mathcal{L}} e^{-pi t^2 |mathbf{y} |^2} le 3/2$, where $t := 10(log n + 2)$. From this we derive bounds on the number of short lattice vectors, which can be viewed as a partial converse to Minkowski’s celebrated first theorem. We also derive a bound on the covering radius.</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"13 1","pages":""},"PeriodicalIF":4.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064088","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}
Pub Date : 2023-11-01DOI: 10.4007/annals.2023.198.3.6
Ionuţ Chifan, Adrian Ioana, Denis Osin, Bin Sun
We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group $G$ in a natural family of wreath-like products with property (T) is W$^*$-superrigid: the group von Neumann algebra $text{L}(G)$ remembers the isomorphism class of $G$. This allows us to provide the first examples (in fact, $2^{aleph_0}$ pairwise non-isomorphic examples) of W$^*$-superrigid groups with property (T).
{"title":"Wreath-like products of groups and their von Neumann algebras I: W^∗-superrigidity","authors":"Ionuţ Chifan, Adrian Ioana, Denis Osin, Bin Sun","doi":"10.4007/annals.2023.198.3.6","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.6","url":null,"abstract":"We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group $G$ in a natural family of wreath-like products with property (T) is W$^*$-superrigid: the group von Neumann algebra $text{L}(G)$ remembers the isomorphism class of $G$. This allows us to provide the first examples (in fact, $2^{aleph_0}$ pairwise non-isomorphic examples) of W$^*$-superrigid groups with property (T).","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"62 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135370613","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}
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square root of the average number of particles, converge to a Gaussian process driven by the fluctuating Boltzmann equation, as predicted by Spohn; (2) large deviations are exponentially small in the average number of particles and are characterized, under regularity assumptions, by a large deviation functional as previously obtained by Rezakhanlou for dynamics with stochastic collisions. The results are valid away from thermal equilibrium, but only for short times. Our strategy is based on uniform a priori bounds on the cumulant generating function, characterizing the fine structure of the small correlations.
{"title":"Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations","authors":"Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella","doi":"10.4007/annals.2023.198.3.3","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.3","url":null,"abstract":"We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square root of the average number of particles, converge to a Gaussian process driven by the fluctuating Boltzmann equation, as predicted by Spohn; (2) large deviations are exponentially small in the average number of particles and are characterized, under regularity assumptions, by a large deviation functional as previously obtained by Rezakhanlou for dynamics with stochastic collisions. The results are valid away from thermal equilibrium, but only for short times. Our strategy is based on uniform a priori bounds on the cumulant generating function, characterizing the fine structure of the small correlations.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"390 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103069","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}
Pub Date : 2023-11-01DOI: 10.4007/annals.2023.198.3.4
Philip Dittmann, Florian Pop
We resolve the Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is an explicit first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.
{"title":"Characterizing finitely generated fields by a single field axiom","authors":"Philip Dittmann, Florian Pop","doi":"10.4007/annals.2023.198.3.4","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.4","url":null,"abstract":"We resolve the Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is an explicit first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"215 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018341","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}
Pub Date : 2023-11-01DOI: 10.4007/annals.2023.198.3.5
José M. Conde-Alonso, Adrián M. González-Pérez, Javier Parcet, Eduardo Tablate
We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers $S_M$ on Schatten $p$-classes which solves a conjecture proposed by Mikael de la Salle. Given $1lt plt infty$, a simple form of our main result for $mathbf{R}^n times mathbf{R}^n$ matrices reads as follows: $$big| S_M colon S_p to S_p big|_{mathrm{cb}} lesssim frac{p^2}{p-1} sum_{|gamma| le [frac{n}{2}] +1} Big| |x-y|^{|gamma|} Big{ big| partial_x^gamma M(x,y) big| + big| partial_y^gamma M(x,y) big| Big} Big|_infty.$$ In this form, it is a full matrix (nonToeplitz/nontrigonometric) amplification of the Hörmander-Mikhlin multiplier theorem, which admits lower fractional differentiability orders $sigma > frac{n}{2}$ as well. It trivially includes Arazy's conjecture for $S_p$-multipliers and extends it to $alpha$-divided differences. It also leads to new Littlewood-Paley characterizations of $S_p$-norms and strong applications in harmonic analysis for nilpotent and high rank simple Lie group algebras.
我们建立了Schatten $p$类上Schur乘子$S_M$有界性的一个意想不到的简单判据，解决了Mikael de la Salle提出的一个猜想。给定$1lt plt infty$，我们对$mathbf{R}^n times mathbf{R}^n$矩阵的主要结果的简单形式如下:$$big| S_M colon S_p to S_p big|_{mathrm{cb}} lesssim frac{p^2}{p-1} sum_{|gamma| le [frac{n}{2}] +1} Big| |x-y|^{|gamma|} Big{ big| partial_x^gamma M(x,y) big| + big| partial_y^gamma M(x,y) big| Big} Big|_infty.$$在这种形式中，它是Hörmander-Mikhlin乘数定理的一个全矩阵(非toeplitz /非三角)放大，它也允许较低的分数阶可微性$sigma > frac{n}{2}$。它简单地包含了Arazy关于$S_p$ -乘数的猜想，并将其扩展到$alpha$ -除差。本文还得到了$S_p$ -范数的新的Littlewood-Paley刻画，并在幂零和高阶单李群代数的调和分析中有了较强的应用。
{"title":"Schur multipliers in Schatten-von Neumann classes","authors":"José M. Conde-Alonso, Adrián M. González-Pérez, Javier Parcet, Eduardo Tablate","doi":"10.4007/annals.2023.198.3.5","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.5","url":null,"abstract":"We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers $S_M$ on Schatten $p$-classes which solves a conjecture proposed by Mikael de la Salle. Given $1lt plt infty$, a simple form of our main result for $mathbf{R}^n times mathbf{R}^n$ matrices reads as follows: $$big| S_M colon S_p to S_p big|_{mathrm{cb}} lesssim frac{p^2}{p-1} sum_{|gamma| le [frac{n}{2}] +1} Big| |x-y|^{|gamma|} Big{ big| partial_x^gamma M(x,y) big| + big| partial_y^gamma M(x,y) big| Big} Big|_infty.$$ In this form, it is a full matrix (nonToeplitz/nontrigonometric) amplification of the Hörmander-Mikhlin multiplier theorem, which admits lower fractional differentiability orders $sigma > frac{n}{2}$ as well. It trivially includes Arazy's conjecture for $S_p$-multipliers and extends it to $alpha$-divided differences. It also leads to new Littlewood-Paley characterizations of $S_p$-norms and strong applications in harmonic analysis for nilpotent and high rank simple Lie group algebras.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135116920","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}
Pub Date : 2023-11-01DOI: 10.4007/annals.2023.198.3.1
Amol Aggarwal
{"title":"Universality for lozenge tiling local statistics","authors":"Amol Aggarwal","doi":"10.4007/annals.2023.198.3.1","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.1","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"64 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135370604","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}
Pub Date : 2023-11-01DOI: 10.4007/annals.2023.198.3.2
Nick Edelen, Luca Spolaor
Hardt-Simon proved that every area-minimizing hypercone $mathbf{C}$ having only an isolated singularity fits into a foliation of $mathbb{R}^{n+1}$ by smooth, area-minimizing hypersurfaces asymptotic to $mathbf{C}$. In this paper we prove that if a stationary $n$-varifold $M$ in the unit ball $B_1 subset mathbb{R}^{n+1}$ lies sufficiently close to a minimizing quadratic cone (for example, the Simons' cone $mathbf{C}^{3,3}$), then $mathrm{spt} M cap B_{1/2}$ is a $C^{1,alpha}$ perturbation of either the cone itself, or some leaf of its associated foliation. In particular, we show that singularities modeled on these cones determine the local structure not only of $M$, but of any nearby minimal surface. Our result also implies the Bernstein-type result of Simon-Solomon, which characterizes area-minimizing hypersurfaces asymptotic to a quadratic cone as either the cone itself, or some leaf of the foliation.
hart - simon证明了每一个只有孤立奇点的面积最小化超锥$mathbf{C}$，都符合一个光滑的、渐近于$mathbf{C}$的面积最小化超曲面的叶状$mathbb{R}^{n+1}$。在本文中，我们证明了如果在单位球$B_1 subset mathbb{R}^{n+1}$中的一个平稳的$n$ -变分$M$足够靠近一个最小化的二次锥(例如，Simons锥$mathbf{C}^{3,3}$)，那么$mathrm{spt} M cap B_{1/2}$是锥本身的一个$C^{1,alpha}$摄动，或者是其相关叶状的一些叶状。特别地，我们证明了在这些锥体上建模的奇点不仅决定了$M$的局部结构，而且决定了任何附近最小表面的局部结构。我们的结果也暗示了Simon-Solomon的bernstein型结果，该结果将渐近于二次锥的面积最小化超曲面刻画为锥本身或叶状叶的某些叶。
{"title":"Regularity of minimal surfaces near quadratic cones","authors":"Nick Edelen, Luca Spolaor","doi":"10.4007/annals.2023.198.3.2","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.2","url":null,"abstract":"Hardt-Simon proved that every area-minimizing hypercone $mathbf{C}$ having only an isolated singularity fits into a foliation of $mathbb{R}^{n+1}$ by smooth, area-minimizing hypersurfaces asymptotic to $mathbf{C}$. In this paper we prove that if a stationary $n$-varifold $M$ in the unit ball $B_1 subset mathbb{R}^{n+1}$ lies sufficiently close to a minimizing quadratic cone (for example, the Simons' cone $mathbf{C}^{3,3}$), then $mathrm{spt} M cap B_{1/2}$ is a $C^{1,alpha}$ perturbation of either the cone itself, or some leaf of its associated foliation. In particular, we show that singularities modeled on these cones determine the local structure not only of $M$, but of any nearby minimal surface. Our result also implies the Bernstein-type result of Simon-Solomon, which characterizes area-minimizing hypersurfaces asymptotic to a quadratic cone as either the cone itself, or some leaf of the foliation.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"681 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018462","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}
Pub Date : 2023-11-01DOI: 10.4007/annals.2023.198.3.7
Georg Schumacher, Hajime Tsuji
{"title":"Retraction: \"Quasi-projectivity of moduli spaces of polarized varieties\"","authors":"Georg Schumacher, Hajime Tsuji","doi":"10.4007/annals.2023.198.3.7","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.7","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135370605","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}
Pub Date : 2023-09-01DOI: 10.4007/annals.2023.198.2.8
Xinyi Yuan, Shou-Wu Zhang
{"title":"Erratum to \"On the averaged Colmez conjecture\"","authors":"Xinyi Yuan, Shou-Wu Zhang","doi":"10.4007/annals.2023.198.2.8","DOIUrl":"https://doi.org/10.4007/annals.2023.198.2.8","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":" ","pages":""},"PeriodicalIF":4.9,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48271079","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}
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