{"title":"The holonomy inverse problem","authors":"Mihajlo Cekić, Thibault Lefeuvre","doi":"10.4171/jems/1409","DOIUrl":"https://doi.org/10.4171/jems/1409","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"7 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139148722","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}
{"title":"Clique factors in pseudorandom graphs","authors":"Patrick Morris","doi":"10.4171/jems/1388","DOIUrl":"https://doi.org/10.4171/jems/1388","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"5 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138967256","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}
{"title":"A Torelli-like theorem for higher-dimensional function fields","authors":"Adam Topaz","doi":"10.4171/jems/1382","DOIUrl":"https://doi.org/10.4171/jems/1382","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"53 36","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138995433","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}
{"title":"Subconvexity bounds for $textrm{GL(3)}times textrm{GL(2)}$ $L$-functions in $textrm{GL(2)}$ spectral aspect","authors":"Sumit Kumar","doi":"10.4171/jems/1383","DOIUrl":"https://doi.org/10.4171/jems/1383","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"146 1‐4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138966927","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}
{"title":"Geometric $L$-packets of Howe-unramified toral supercuspidal representations","authors":"Charlotte Chan, Masao Oi","doi":"10.4171/jems/1396","DOIUrl":"https://doi.org/10.4171/jems/1396","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"46 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138966805","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}
. In this paper, we obtain sharp estimates for the rate of propagation of the Fisher-KPP equation with nonlocal diffusion and free boundaries. The nonlocal diffusion operator is given by (cid:82) R J ( x − y ) u ( t, y ) dy − u ( t, x ), and our estimates hold for some typical classes of kernel functions J ( x ). For example, if for | x | (cid:29) 1 the kernel function satisfies J ( x ) ∼ | x | − γ with γ > 1, then it follows from [17] that there is a finite spreading speed when γ > 2, namely the free boundary x = h ( t ) satisfies lim t →∞ h ( t ) /t = c 0 for some uniquely determined positive constant c 0 depending on J , and when γ ∈ (1 , 2], lim t →∞ h ( t ) /t = ∞ ; the estimates in the current paper imply that, for t (cid:29) 1, c 0 t − h ( t ) ∼ 1 when γ > 3 ln t when γ = 3 , t 3 − γ when γ ∈ (2 , 3) , and h ( t ) ∼ (cid:26) t ln t when γ = 2 , t 1 / ( γ − 1) when γ ∈ (1 , 2) . Our approach is based on subtle integral estimates and constructions of upper and lower solutions, which rely crucially on guessing correctly the order of growth of the term to be estimated. The techniques developed here lay the ground for extensions to more general situations.
.在本文中，我们得到了具有非局部二重扩散和自由边界的 Fisher-KPP 方程传播速度的精确估计值。非局部扩散算子由 (cid:82) R J ( x - y ) u ( t, y ) dy - u ( t, x ) 给出，我们的估计值对于一些典型的核函数 J ( x ) 类是成立的。例如，如果对于 | x | (cid：29) 1 的核函数满足 J ( x ) ∼ | x | - γ，且 γ > 1，那么根据[17]，当 γ > 2 时，存在一个有限的扩散速度、即自由边界 x = h ( t ) 对于某个取决于 J 的唯一确定的正常数 c 0 满足 lim t →∞ h ( t ) /t = c 0，而当γ∈（1 , 2]时，lim t →∞ h ( t ) /t = ∞；本文的估计意味着，对于 t （cid：29) 1 时，当 γ > 3 时，c 0 t - h ( t ) ∼ 1 ；当 γ = 3 时，t 3 - γ ；当 γ ∈ (2 , 3) 时，h ( t ) ∼ (cid:26) t ；当 γ = 2 时，t 1 / ( γ - 1) ；当 γ ∈ (1 , 2) 时，h ( t ) ∼ (cid:26) t 。我们的方法基于微妙的积分估计和上下限解的构造，其关键在于正确猜测待估计项的增长阶数。这里开发的技术为扩展到更一般的情况奠定了基础。
{"title":"Rate of propagation for the Fisher-KPP equation with nonlocal diffusion and free boundaries","authors":"Yihong Du, W. Ni","doi":"10.4171/jems/1392","DOIUrl":"https://doi.org/10.4171/jems/1392","url":null,"abstract":". In this paper, we obtain sharp estimates for the rate of propagation of the Fisher-KPP equation with nonlocal diffusion and free boundaries. The nonlocal diffusion operator is given by (cid:82) R J ( x − y ) u ( t, y ) dy − u ( t, x ), and our estimates hold for some typical classes of kernel functions J ( x ). For example, if for | x | (cid:29) 1 the kernel function satisfies J ( x ) ∼ | x | − γ with γ > 1, then it follows from [17] that there is a finite spreading speed when γ > 2, namely the free boundary x = h ( t ) satisfies lim t →∞ h ( t ) /t = c 0 for some uniquely determined positive constant c 0 depending on J , and when γ ∈ (1 , 2], lim t →∞ h ( t ) /t = ∞ ; the estimates in the current paper imply that, for t (cid:29) 1, c 0 t − h ( t ) ∼ 1 when γ > 3 ln t when γ = 3 , t 3 − γ when γ ∈ (2 , 3) , and h ( t ) ∼ (cid:26) t ln t when γ = 2 , t 1 / ( γ − 1) when γ ∈ (1 , 2) . Our approach is based on subtle integral estimates and constructions of upper and lower solutions, which rely crucially on guessing correctly the order of growth of the term to be estimated. The techniques developed here lay the ground for extensions to more general situations.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"50 16","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138995829","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}
M. A. D. de Cataldo, D. Maulik, Junliang Shen, Siqing Zhang
{"title":"Cohomology of the moduli of Higgs bundles on a curve via positive characteristic","authors":"M. A. D. de Cataldo, D. Maulik, Junliang Shen, Siqing Zhang","doi":"10.4171/jems/1393","DOIUrl":"https://doi.org/10.4171/jems/1393","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"48 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138967703","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}
Eli Glasner, Wen Huang, Song Shao, Benjamin Weiss, Xiangdong Ye
We prove that the maximal infinite step pro-nilfactor $X_infty$ of a minimal dynamical system $(X,T)$ is the topological characteristic factor in a certain sense. Namely, we show that by an almost one to one modification of $pi:X rightarrow X_infty$, the induced open extension $pi^*:X^* rightarrow X^*_infty$ has the following property: for $x$ in a dense $G_delta$ set of $X^*$, the orbit closure $L_x=overline{mathcal{O}}((x,x,ldots,x), Ttimes T^2times ldots times T^d)$ is $(pi^*)^{(d)}$-saturated, i.e. $L_x=((pi^*)^{(d)})^{-1}(pi^*)^{(d)}(L_x)$.
{"title":"Topological characteristic factors and nilsystems","authors":"Eli Glasner, Wen Huang, Song Shao, Benjamin Weiss, Xiangdong Ye","doi":"10.4171/jems/1379","DOIUrl":"https://doi.org/10.4171/jems/1379","url":null,"abstract":"We prove that the maximal infinite step pro-nilfactor $X_infty$ of a minimal dynamical system $(X,T)$ is the topological characteristic factor in a certain sense. Namely, we show that by an almost one to one modification of $pi:X rightarrow X_infty$, the induced open extension $pi^*:X^* rightarrow X^*_infty$ has the following property: for $x$ in a dense $G_delta$ set of $X^*$, the orbit closure $L_x=overline{mathcal{O}}((x,x,ldots,x), Ttimes T^2times ldots times T^d)$ is $(pi^*)^{(d)}$-saturated, i.e. $L_x=((pi^*)^{(d)})^{-1}(pi^*)^{(d)}(L_x)$. ","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"569 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870959","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}
Jason Bell, Keping Huang, Wayne Peng, Thomas Tucker
We prove an analog of the Tits alternative for endomorphisms of $mathbb{P}^1$. In particular, we show that if $S$ is a finitely generated semigroup of endomorphisms of $mathbb{P}^1$ over $mathbb{C}$, then either $S$ has polynomially bounded growth or $S$ contains a nonabelian free semigroup. We also show that if $f$ and $g$ are polarizable maps over any field of any characteristic and $operatorname{Prep}(f) not= operatorname{Prep}(g)$, then for all sufficiently large $j$, the semigroup $langle f^j, g^j rangle$ is a free semigroup on two generators.
{"title":"A Tits alternative for endomorphisms of the projective line","authors":"Jason Bell, Keping Huang, Wayne Peng, Thomas Tucker","doi":"10.4171/jems/1376","DOIUrl":"https://doi.org/10.4171/jems/1376","url":null,"abstract":"We prove an analog of the Tits alternative for endomorphisms of $mathbb{P}^1$. In particular, we show that if $S$ is a finitely generated semigroup of endomorphisms of $mathbb{P}^1$ over $mathbb{C}$, then either $S$ has polynomially bounded growth or $S$ contains a nonabelian free semigroup. We also show that if $f$ and $g$ are polarizable maps over any field of any characteristic and $operatorname{Prep}(f) not= operatorname{Prep}(g)$, then for all sufficiently large $j$, the semigroup $langle f^j, g^j rangle$ is a free semigroup on two generators.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135808401","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 prove a sharp stability result for the Brunn–Minkowski inequality for $A,Bsubsetmathbb{R}^2$. Assuming that the Brunn–Minkowski deficit $delta=|A+B|^{1/2}/(|A|^{1/2}+|B|^{1/2})-1$ is sufficiently small in terms of $t=|A|^{1/2}/(|A|^{1/2}+|B|^{1/2})$, there exist homothetic convex sets $K_A supset A$ and $K_Bsupset B$ such that $frac{|K_Asetminus A|}{|A|}+frac{|K_Bsetminus B|}{|B|} le C t^{-{1/2}}delta^{1/2}$. The key ingredient is to show for every $epsilon,t>0$, if $delta$ is sufficiently small then $|!operatorname{co}(A+B)setminus (A+B)|le (1+epsilon)(|!operatorname{co}(A)setminus A|+|!operatorname{co}(B)setminus B|)$.
对于$A,Bsubsetmathbb{R}^2$，我们证明了Brunn-Minkowski不等式的一个尖锐的稳定性结果。假设Brunn-Minkowski赤字$delta=|A+B|^{1/2}/(|A|^{1/2}+|B|^{1/2})-1$在$t=|A|^{1/2}/(|A|^{1/2}+|B|^{1/2})$上足够小，则存在齐次凸集$K_A supset A$和$K_Bsupset B$，使得$frac{|K_Asetminus A|}{|A|}+frac{|K_Bsetminus B|}{|B|} le C t^{-{1/2}}delta^{1/2}$。关键是要显示对于每个$epsilon,t>0$，如果$delta$足够小，那么$|!operatorname{co}(A+B)setminus (A+B)|le (1+epsilon)(|!operatorname{co}(A)setminus A|+|!operatorname{co}(B)setminus B|)$。
{"title":"Sharp quantitative stability of the planar Brunn–Minkowski inequality","authors":"Peter van Hintum, Hunter Spink, Marius Tiba","doi":"10.4171/jems/1372","DOIUrl":"https://doi.org/10.4171/jems/1372","url":null,"abstract":"We prove a sharp stability result for the Brunn–Minkowski inequality for $A,Bsubsetmathbb{R}^2$. Assuming that the Brunn–Minkowski deficit $delta=|A+B|^{1/2}/(|A|^{1/2}+|B|^{1/2})-1$ is sufficiently small in terms of $t=|A|^{1/2}/(|A|^{1/2}+|B|^{1/2})$, there exist homothetic convex sets $K_A supset A$ and $K_Bsupset B$ such that $frac{|K_Asetminus A|}{|A|}+frac{|K_Bsetminus B|}{|B|} le C t^{-{1/2}}delta^{1/2}$. The key ingredient is to show for every $epsilon,t>0$, if $delta$ is sufficiently small then $|!operatorname{co}(A+B)setminus (A+B)|le (1+epsilon)(|!operatorname{co}(A)setminus A|+|!operatorname{co}(B)setminus B|)$.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"30 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972736","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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