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Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups 动机函数，可积性，及其在$p$-进群调和分析中的应用
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-10-01 DOI: 10.3934/ERA.2014.21.137
R. Cluckers, J. Gordon, Immanuel Halupczok
{"title":"Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups","authors":"R. Cluckers, J. Gordon, Immanuel Halupczok","doi":"10.3934/ERA.2014.21.137","DOIUrl":"https://doi.org/10.3934/ERA.2014.21.137","url":null,"abstract":"We provide a short and self-contained overview of the techniques based on motivic integration as they are applied in harmonic analysis on p-adic groups; our target audience is mainly representation theorists with no back- ground in model theory (and model theorists with an interest in recent ap- plications of motivic integration in representation theory, though we do not provide any representation theory background). We aim to give a fairly com- prehensive survey of the results in harmonic analysis that were proved by such techniques in the last ten years, with emphasis on the most recent techniques and applications from (13), (8), and (32, Appendix B).","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"21 1","pages":"137-152"},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
An arithmetic ball quotient surface whose Albanese variety is not of CM type 一个不属于CM型的算术球商曲面
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-09-01 DOI: 10.3934/ERA.2014.21.132
Chad Schoen
{"title":"An arithmetic ball quotient surface whose Albanese variety is not of CM type","authors":"Chad Schoen","doi":"10.3934/ERA.2014.21.132","DOIUrl":"https://doi.org/10.3934/ERA.2014.21.132","url":null,"abstract":"An example is given of a compact quotient of the unit ball in $mathbb{C}^2$ by an arithmetic group acting freely such that the Albanese variety is not of CM type. \u0000Such examples do not exist for congruence subgroups.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"21 1","pages":"132-136"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3934/ERA.2014.21.132","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A sharp Sobolev-Strichartz estimate for the wave equation 波动方程的Sobolev-Strichartz估计
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-07-07 DOI: 10.3934/ERA.2015.22.46
N. Bez, Chris Jeavons
{"title":"A sharp Sobolev-Strichartz estimate for the wave equation","authors":"N. Bez, Chris Jeavons","doi":"10.3934/ERA.2015.22.46","DOIUrl":"https://doi.org/10.3934/ERA.2015.22.46","url":null,"abstract":"We calculate the the sharp constant and characterize the extremal initial data in $dot{H}^{frac{3}{4}} times dot{H}^{-frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four spatial dimensions.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"22 1","pages":"46-54"},"PeriodicalIF":0.0,"publicationDate":"2014-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70234044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Number of extremal subsets in Alexandrov spaces and rigidity Alexandrov空间的极值子集数与刚性
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-07-01 DOI: 10.3934/ERA.2014.21.120
N. Lebedeva
{"title":"Number of extremal subsets in Alexandrov spaces and rigidity","authors":"N. Lebedeva","doi":"10.3934/ERA.2014.21.120","DOIUrl":"https://doi.org/10.3934/ERA.2014.21.120","url":null,"abstract":"In this paper we announce the following result. We show that any $n$-dimensional nonnegatively curved Alexandrov space with the maximal possible number of extremal points is isometric to a quotient space of $mathbb{R}^n$ by an action of a crystallographic group. We describe all such actions. We start with a history, results and open questions concerning estimates on the number of extremal subsets in Alexandrov spaces. Then we give the plan of the proof of our result; the complete proof will published elsewhere.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"44 1","pages":"120-125"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70232961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
THE APPROXIMATE LOEBL-KOMLOS-SOS CONJECTURE AND EMBEDDING TREES IN SPARSE GRAPHS 近似loeble - komlos - sos猜想及稀疏图中的嵌入树
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-06-16 DOI: 10.3934/era.2015.22.1
J. Hladký, Diana Piguet, M. Simonovits, M. Stein, E. Szemerédi
{"title":"THE APPROXIMATE LOEBL-KOMLOS-SOS CONJECTURE AND EMBEDDING TREES IN SPARSE GRAPHS","authors":"J. Hladký, Diana Piguet, M. Simonovits, M. Stein, E. Szemerédi","doi":"10.3934/era.2015.22.1","DOIUrl":"https://doi.org/10.3934/era.2015.22.1","url":null,"abstract":"Loebl, Komlos and Sos conjectured that every $n$-vertex graph $G$ with at least $n/2$ vertices \u0000of degree at least $k$ contains each tree $T$ of order $k+1$ as a \u0000subgraph. We give a sketch of a proof of the approximate version of this conjecture for large values of $k$. \u0000 \u0000For our proof, we use a structural decomposition which can be seen as an analogue of Szemeredi's regularity lemma for possibly very sparse graphs. With this tool, each graph can be decomposed into four parts: a set of vertices of huge degree, regular pairs (in the sense of the regularity lemma), and two other objects each exhibiting certain expansion properties. We then exploit the properties of each of the parts of $G$ to embed a given tree $T$. \u0000 \u0000The purpose of this note is to highlight the key steps of our proof. Details can be found in [arXiv:1211.3050].","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"8 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Fixed frequency eigenfunction immersions and supremum norms of random waves 随机波的定频特征函数浸没和上模
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-06-07 DOI: 10.3934/era.2015.22.76
Y. Canzani, B. Hanin
{"title":"Fixed frequency eigenfunction immersions and supremum norms of random waves","authors":"Y. Canzani, B. Hanin","doi":"10.3934/era.2015.22.76","DOIUrl":"https://doi.org/10.3934/era.2015.22.76","url":null,"abstract":"A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"22 1","pages":"76-86"},"PeriodicalIF":0.0,"publicationDate":"2014-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70234085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
ON EXISTENCE OF PI-EXPONENTS OF CODIMENSION GROWTH 余维增长的指数的存在性
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-06-01 DOI: 10.3934/ERA.2014.21.113
M. Zaicev
{"title":"ON EXISTENCE OF PI-EXPONENTS OF CODIMENSION GROWTH","authors":"M. Zaicev","doi":"10.3934/ERA.2014.21.113","DOIUrl":"https://doi.org/10.3934/ERA.2014.21.113","url":null,"abstract":"We construct a family of examples of non-associative algebras ${R_alpha ,vert, 1<alphainmathbb R}$ such that $underline{exp}(R_alpha)=1$, $overline{exp}(R_alpha)=alpha$. In particular, it follows that for any $R_alpha$, an ordinary PI-exponent of codimension growth does not exist.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"128 1","pages":"113-119"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70232949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Pseudo-Anosov eigenfoliations on Panov planes Panov平面上的伪anosov特征叶
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-05-01 DOI: 10.3934/ERA.2014.21.89
Christy Johnson, Martin Schmoll
{"title":"Pseudo-Anosov eigenfoliations on Panov planes","authors":"Christy Johnson, Martin Schmoll","doi":"10.3934/ERA.2014.21.89","DOIUrl":"https://doi.org/10.3934/ERA.2014.21.89","url":null,"abstract":"We study dynamical properties of direction foliations on the complex plane pulled back from \u0000direction foliations on a half-translation torus $T$, i.e., a torus equipped with a strict \u0000and integrable quadratic differential. \u0000If the torus $T$ admits a pseudo-Anosov map we give a homological criterion for the appearance of dense leaves and leaves with bounded deviation on the universal covering of $T$, called Panov plane. \u0000Our result generalizes Dmitri Panov's explicit construction of dense leaves for certain \u0000arithmetic half-translation tori [33]. Certain Panov planes are related to \u0000the polygonal table of the periodic wind-tree model. In fact, we show that the dynamics \u0000on periodic wind-tree billiards can be converted to the dynamics on a pair of singular planes. \u0000   \u0000Possible strategies to generalize our main dynamical result to larger sets \u0000of directions are discussed. Particularly we include recent results \u0000of Frączek and Ulcigrai [17, 18] and Delecroix [6] \u0000for the wind-tree model. Implicitly Panov planes appear in Frączek and Schmoll [15], \u0000where the authors consider Eaton Lens distributions.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"21 1","pages":"89-108"},"PeriodicalIF":0.0,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
FROM LOCAL TO GLOBAL EQUILIBRIUM STATES: THERMODYNAMIC FORMALISM VIA AN INDUCING SCHEME 从局部到全局平衡状态:通过归纳方案的热力学形式
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-05-01 DOI: 10.3934/ERA.2014.21.72
R. Leplaideur
{"title":"FROM LOCAL TO GLOBAL EQUILIBRIUM STATES: THERMODYNAMIC FORMALISM VIA AN INDUCING SCHEME","authors":"R. Leplaideur","doi":"10.3934/ERA.2014.21.72","DOIUrl":"https://doi.org/10.3934/ERA.2014.21.72","url":null,"abstract":"We present a method to construct equilibrium states via inducing. This method can be used for some non-uniformly hyperbolic dynamical systems and for non-Holder continuous potentials. It allows us to prove the existence of phase transition.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"21 1","pages":"72-79"},"PeriodicalIF":0.0,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone 具有有理多面体伪有效锥的代数曲面上的Minkowski基
Electronic Research Announcements in Mathematical Sciences Pub Date : 2014-01-02 DOI: 10.3934/era.2014.21.126
Piotr Pokora, T. Szemberg
{"title":"Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone","authors":"Piotr Pokora, T. Szemberg","doi":"10.3934/era.2014.21.126","DOIUrl":"https://doi.org/10.3934/era.2014.21.126","url":null,"abstract":"The purpose of this note is to study the number of elements in Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"21 1","pages":"126-131"},"PeriodicalIF":0.0,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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