Advances in Mathematics最新文献_第4页

Positivity in weighted flag varieties 加权旗品种的正性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-04 DOI: 10.1016/j.aim.2026.110798

William Graham, Scott Joseph Larson

{"title":"Positivity in weighted flag varieties","authors":"William Graham, Scott Joseph Larson","doi":"10.1016/j.aim.2026.110798","DOIUrl":"10.1016/j.aim.2026.110798","url":null,"abstract":"<div><div>We study the torus-equivariant cohomology of weighted flag varieties, and prove a positivity property in the equivariant cohomology and Chow groups of weighted flag varieties, analogous to the non-weighted positivity proved in <span><span>[23]</span></span>. Our result strengthens and generalizes the positivity proved for weighted Grassmannians by Abe-Matsumura <span><span>[1]</span></span>. The positivity property is expressed in terms of weighted roots, which are used to describe weights of torus equivariant curves in weighted flag varieties. This provides a geometric interpretation of the parameters used in <span><span>[1]</span></span>. We approach weighted flag varieties from a uniform Lie-theoretic point of view, providing a more general definition than has appeared previously, and prove other general results about weighted flag varieties in this setting, including a Borel presentation of the equivariant cohomology. In addition, we generalize some results obtained for weighted Grassmannians or more generally type <em>A</em> (<span><span>[1]</span></span>, <span><span>[6]</span></span>); in particular, we obtain descriptions of restrictions to fixed points, the GKM description of the cohomology, and a weighted Chevalley formula.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"489 ","pages":"Article 110798"},"PeriodicalIF":1.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174138","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: 0

Erratum to “Isometric embeddings of Teichmüller spaces are covering constructions” “teichmller空间的等距嵌入覆盖了建筑”的勘误

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.aim.2026.110831

Frederik Benirschke, Carlos A. Serván

引用次数: 0

Formally integrable structures II. Division problem 形式可积结构2。部门问题

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-12 DOI: 10.1016/j.aim.2026.110861

Qingchun Ji , Jun Yao

引用次数: 0

A1-homotopy type of A2∖{(0,0)} A2∈{(0,0)}的a1 -同伦型

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.aim.2026.110806

Utsav Choudhury, Biman Roy

引用次数: 0

Existence and non-uniqueness of weak solutions with continuous energy to the 3D deterministic and stochastic Navier-Stokes equations 三维确定性随机Navier-Stokes方程连续能量弱解的存在性与非唯一性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-13 DOI: 10.1016/j.aim.2026.110845

Alexey Cheskidov , Zirong Zeng , Deng Zhang

引用次数: 0

Real spectrum compactification of Hitchin components, Weyl chamber valued lengths, and dual spaces 希钦分量、Weyl室值长度和对偶空间的实谱紧化

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-01-27 DOI: 10.1016/j.aim.2026.110802

Xenia Flamm

{"title":"Real spectrum compactification of Hitchin components, Weyl chamber valued lengths, and dual spaces","authors":"Xenia Flamm","doi":"10.1016/j.aim.2026.110802","DOIUrl":"10.1016/j.aim.2026.110802","url":null,"abstract":"<div><div>The main result of this article is that Hitchin representations over real closed field extensions <span><math><mi>F</mi></math></span> of <span><math><mi>R</mi></math></span> correspond precisely to those representations of the fundamental group of a closed surface into <span><math><mtext>PSL</mtext><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> that are conjugate to <span><math><mi>F</mi></math></span>-positive representations, i.e. representations that admit an equivariant limit map from the set of fixed points in the boundary of the universal cover of the surface into the set of full flags in <span><math><msup><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> satisfying specific positivity properties. As the theorem treats general real closed fields, and not only the reals, the tools of analysis are not available. Instead, our proof is based on the Tarski–Seidenberg transfer principle and a multiplicative version of the Bonahon–Dreyer coordinates.</div><div>We use this result to prove that <span><math><mi>F</mi></math></span>-positive representations form semi-algebraically connected components of the space of all representations, that consist entirely of injective and discrete representations, which are positively hyperbolic and weakly dynamics-preserving over <span><math><mi>F</mi></math></span>. Furthermore, we show how to associate intersection geodesic currents to <span><math><mi>F</mi></math></span>-positive representations, and conclude with applications to the Weyl chamber length compactification and to dual spaces of geodesic currents.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"489 ","pages":"Article 110802"},"PeriodicalIF":1.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080758","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: 0

Iterated function systems of holomorphic maps 全纯映射的迭代函数系统

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-04 DOI: 10.1016/j.aim.2026.110818

Marco Abate, Ian Short

引用次数: 0

Quantization of the Willmore energy in Riemannian manifolds 黎曼流形中Willmore能量的量子化

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.aim.2026.110789

Alexis Michelat , Andrea Mondino

引用次数: 0

Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement 广义算子的稀疏Gabor表示：受控指数衰减和Schrödinger约束

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-02 DOI: 10.1016/j.aim.2026.110828

Elena Cordero , Gianluca Giacchi , Edoardo Pucci , S. Ivan Trapasso

{"title":"Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement","authors":"Elena Cordero , Gianluca Giacchi , Edoardo Pucci , S. Ivan Trapasso","doi":"10.1016/j.aim.2026.110828","DOIUrl":"10.1016/j.aim.2026.110828","url":null,"abstract":"<div><div>Motivated by the phase space analysis of Schrödinger evolution operators, in this paper we investigate how metaplectic operators are approximately diagonalized along the corresponding symplectic flows by exponentially localized Gabor wave packets. Quantitative bounds for the matrix coefficients arising in the Gabor wave packet decomposition of such operators are established, revealing precise exponential decay rates together with subtler dispersive and spreading phenomena. To this end, we present several novel results concerning the time-frequency analysis of functions with controlled Gelfand-Shilov regularity, which are of independent interest.</div><div>As a byproduct, we generalize Vemuri's Gaussian confinement results for the solutions of the quantum harmonic oscillator in two respects, namely by encompassing general exponential decay rates as well as arbitrary quadratic Schrödinger propagators. In particular, we extensively discuss some prominent models such as the harmonic oscillator, the free particle in a constant magnetic field and fractional Fourier transforms.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110828"},"PeriodicalIF":1.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174566","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: 0

Betti number bounds for varieties and exponential sums 变量和指数和的Betti数界

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2026-04-01 Epub Date: 2026-02-12 DOI: 10.1016/j.aim.2026.110852

Daqing Wan , Dingxin Zhang

引用次数: 0