Acta Mathematica最新文献_第3页

Noncollision singularities in a planar 4-body problem 平面四体问题的非碰撞奇异性

IF 3.7 1区数学

Acta Mathematica Pub Date : 2020-01-01 DOI: 10.4310/acta.2020.v224.n2.a2

Jinxin Xue

引用次数: 4

Carathéodory completeness on the plane 在平面上的carathimodory完备性

IF 3.7 1区数学

Acta Mathematica Pub Date : 2020-01-01 DOI: 10.4467/20843828am.19.002.12110

A. Edigarian

引用次数: 1

Local homology and Serre categories 局部同源性与Serre范畴

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-12-17 DOI: 10.4467/20843828am.19.001.12109

Zahra Barqsouz, S. O. Faramarzi

引用次数: 0

Generalized Isoperimetric FVPs Via Caputo Approach 基于Caputo方法的广义等周fvp

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-12-17 DOI: 10.4467/20843828am.19.003.12111

Amele Taieb, Z. Dahmani

引用次数: 1

Soliton resolution for the radial critical wave equation in all odd space dimensions 径向临界波方程在所有奇空间维度上的孤立子分辨率

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-12-16 DOI: 10.4310/acta.2023.v230.n1.a1

Thomas Duyckaerts, C. Kenig, F. Merle

引用次数: 15

Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ 半线性椭圆方程的稳定解在维数$9$之前是光滑的

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-07-22 DOI: 10.4310/acta.2020.v224.n2.a1

X. Cabré, A. Figalli, Xavier Ros-Oton, J. Serra

引用次数: 55

A transcendental dynamical degree 超越动力度

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-07-01 DOI: 10.4310/ACTA.2020.V225.N2.A1

J. Bell, J. Diller, Mattias Jonsson

引用次数: 16

Convergence of uniform triangulations under the Cardy embedding Cardy嵌入下一致三角剖分的收敛性

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-05-30 DOI: 10.4310/acta.2023.v230.n1.a2

N. Holden, Xin Sun

引用次数: 40

The Mirković–Vilonen basis and Duistermaat–Heckman measures Mirković-Vilonen基础和Duistermaat-Heckman测量

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-05-21 DOI: 10.4310/acta.2021.v227.n1.a1

Pierre Baumann, J. Kamnitzer, A. Knutson

{"title":"The Mirković–Vilonen basis and Duistermaat–Heckman measures","authors":"Pierre Baumann, J. Kamnitzer, A. Knutson","doi":"10.4310/acta.2021.v227.n1.a1","DOIUrl":"https://doi.org/10.4310/acta.2021.v227.n1.a1","url":null,"abstract":"Using the geometric Satake correspondence, the Mirkovic-Vilonen cycles in the affine Grasssmannian give bases for representations of a semisimple group G . We prove that these bases are \"perfect\", i.e. compatible with the action of the Chevelley generators of the positive half of the Lie algebra g. We compute this action in terms of intersection multiplicities in the affine Grassmannian. We prove that these bases stitch together to a basis for the algebra C[N] of regular functions on the unipotent subgroup. We compute the multiplication in this MV basis using intersection multiplicities in the Beilinson-Drinfeld Grassmannian, thus proving a conjecture of Anderson. In the third part of the paper, we define a map from C[N] to a convolution algebra of measures on the dual of the Cartan subalgebra of g. We characterize this map using the universal centralizer space of G. We prove that the measure associated to an MV basis element equals the Duistermaat-Heckman measure of the corresponding MV cycle. This leads to a proof of a conjecture of Muthiah. Finally, we use the map to measures to compare the MV basis and Lusztig's dual semicanonical basis. We formulate conjectures relating the algebraic invariants of preprojective algebra modules (which underlie the dual semicanonical basis) and geometric invariants of MV cycles. In the appendix, we use these ideas to prove that the MV basis and the dual semicanonical basis do not coincide in SL_6.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45929406","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: 19

The Fuglede conjecture for convex domains is true in all dimensions 凸域的Fuglede猜想在所有维度上都是正确的

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-04-28 DOI: 10.4310/ACTA.2022.v228.n2.a3

Nir Lev, M. Matolcsi

{"title":"The Fuglede conjecture for convex domains is true in all dimensions","authors":"Nir Lev, M. Matolcsi","doi":"10.4310/ACTA.2022.v228.n2.a3","DOIUrl":"https://doi.org/10.4310/ACTA.2022.v228.n2.a3","url":null,"abstract":"A set $Omega subset mathbb{R}^d$ is said to be spectral if the space $L^2(Omega)$ has an orthogonal basis of exponential functions. A conjecture due to Fuglede (1974) stated that $Omega$ is a spectral set if and only if it can tile the space by translations. While this conjecture was disproved for general sets, it has long been known that for a convex body $Omega subset mathbb{R}^d$ the \"tiling implies spectral\" part of the conjecture is in fact true. \u0000To the contrary, the \"spectral implies tiling\" direction of the conjecture for convex bodies was proved only in $mathbb{R}^2$, and also in $mathbb{R}^3$ under the a priori assumption that $Omega$ is a convex polytope. In higher dimensions, this direction of the conjecture remained completely open (even in the case when $Omega$ is a polytope) and could not be treated using the previously developed techniques. \u0000In this paper we fully settle Fuglede's conjecture for convex bodies affirmatively in all dimensions, i.e. we prove that if a convex body $Omega subset mathbb{R}^d$ is a spectral set then it can tile the space by translations. To prove this we introduce a new technique, involving a construction from crystallographic diffraction theory, which allows us to establish a geometric \"weak tiling\" condition necessary for a set $Omega subset mathbb{R}^d$ to be spectral.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2019-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47687210","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: 44