Forum of Mathematics Pi最新文献_第5页

Local newforms for the general linear groups over a non-archimedean local field 非阿基米德局部域上一般线性群的局部新形式

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-10-18 DOI: 10.1017/fmp.2022.17

Hiraku Atobe, S. Kondo, S. Yasuda

引用次数: 8

Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension 局部上同调、Du-Bois复形和局部上同维上的Hodge滤波

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-08-11 DOI: 10.1017/fmp.2022.15

M. Mustaţă, M. Popa

引用次数: 14

On the Torelli Lie algebra 关于Torelli Lie代数

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-06-30 DOI: 10.1017/fmp.2023.10

A. Kupers, O. Randal-Williams

引用次数: 3

Combinatorial and harmonic-analytic methods for integer tilings 整数平铺的组合与谐波解析方法

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-06-26 DOI: 10.1017/fmp.2022.3

I. Łaba, Itay Londner

{"title":"Combinatorial and harmonic-analytic methods for integer tilings","authors":"I. Łaba, Itay Londner","doi":"10.1017/fmp.2022.3","DOIUrl":"https://doi.org/10.1017/fmp.2022.3","url":null,"abstract":"Abstract A finite set of integers A tiles the integers by translations if $mathbb {Z}$ can be covered by pairwise disjoint translated copies of A. Restricting attention to one tiling period, we have $Aoplus B=mathbb {Z}_M$ for some $Min mathbb {N}$ and $Bsubset mathbb {Z}$. This can also be stated in terms of cyclotomic divisibility of the mask polynomials $A(X)$ and $B(X)$ associated with A and B. In this article, we introduce a new approach to a systematic study of such tilings. Our main new tools are the box product, multiscale cuboids and saturating sets, developed through a combination of harmonic-analytic and combinatorial methods. We provide new criteria for tiling and cyclotomic divisibility in terms of these concepts. As an application, we can determine whether a set A containing certain configurations can tile a cyclic group $mathbb {Z}_M$, or recover a tiling set based on partial information about it. We also develop tiling reductions where a given tiling can be replaced by one or more tilings with a simpler structure. The tools introduced here are crucial in our proof in [24] that all tilings of period $(pqr)^2$, where $p,q,r$ are distinct odd primes, satisfy a tiling condition proposed by Coven and Meyerowitz [2].","PeriodicalId":56024,"journal":{"name":"Forum of Mathematics Pi","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43909505","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: 11

Quantitative Heegaard Floer cohomology and the Calabi invariant 定量Heegaard-Floer上同调与Calabi不变量

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-05-23 DOI: 10.1017/fmp.2022.18

Daniel Cristofaro-Gardiner, Vincent Humilière, C. Y. Mak, Sobhan Seyfaddini, I. Smith

{"title":"Quantitative Heegaard Floer cohomology and the Calabi invariant","authors":"Daniel Cristofaro-Gardiner, Vincent Humilière, C. Y. Mak, Sobhan Seyfaddini, I. Smith","doi":"10.1017/fmp.2022.18","DOIUrl":"https://doi.org/10.1017/fmp.2022.18","url":null,"abstract":"Abstract We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, we resolve several open questions from topological surface dynamics and continuous symplectic topology: We show that the group of Hamiltonian homeomorphisms of any compact surface with (possibly empty) boundary is not simple; we extend the Calabi homomorphism to the group of hameomorphisms constructed by Oh and Müller, and we construct an infinite-dimensional family of quasi-morphisms on the group of area and orientation preserving homeomorphisms of the two-sphere. Our invariants are inspired by recent work of Polterovich and Shelukhin defining and applying spectral invariants, via orbifold Floer homology, for links composed of parallel circles in the two-sphere. A particular feature of our work is that it avoids the orbifold setting and relies instead on ‘classical’ Floer homology. This not only substantially simplifies the technical background but seems essential for some aspects (such as the application to constructing quasi-morphisms).","PeriodicalId":56024,"journal":{"name":"Forum of Mathematics Pi","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44250367","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: 13

Sharp smoothing properties of averages over curves 曲线上平均值的平滑特性

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-05-04 DOI: 10.1017/fmp.2023.2

Hyerim Ko, Sanghyuk Lee, Sewook Oh

引用次数: 9

The existence of the Kähler–Ricci soliton degeneration Kähler–Ricci孤子退化的存在性

IF 2.3 1区数学

Forum of Mathematics Pi Pub Date : 2021-03-29 DOI: 10.1017/fmp.2023.5

Harold Blum, Yuchen Liu, Chenyang Xu, Ziquan Zhuang

引用次数: 17

A Proof of the Extended Delta Conjecture 扩展Delta猜想的一个证明