FRG Collaborative Research: Homological Mirror Symmetry and its applications

FRG合作研究:同调镜像对称及其应用

基本信息

  • 批准号:
    0652620
  • 负责人:
  • 金额:
    --
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2007
  • 资助国家:
    美国
  • 起止时间:
    2007-07-15 至 2010-06-30
  • 项目状态:
    已结题

项目摘要

The main aim of this collaborative project is an in-depth study of the homological mirror symmetry conjecture. Auroux, Katzarkov, Kontsevich, Orlov and Seidel will lead a concerted effort to formulate and understand homological mirror symmetry in systematic manner, and extend it to varieties of general type and to noncommutative varieties. This will require some foundational work in homological algebra, noncommutative geometry, and symplectic geometry. Another goal is to investigate applications of mirror symmetry to classical problems in algebraic geometry (for example studying the rationality of certain algebraic varieties) and symplectic topology (in particular, Lagrangian submanifolds). From a wider perspective, the project aims to provide a mathematical counterpart to some recent advances in theoretical physics. The contribution that mathematics can make is to verify the soundness and consistency of physical intuition, and to prepare the general ground on which further development can occur. This is particularly important in those situations where developments in physics suggest the presence of deep and complex structures, which are difficult to detect by direct experiment. At the same time, this effort will make it possible to answer some purely mathematical (geometric) questions, some of which have been open for a long time. The collaborative effort will be carried out through regular meetings and workshops, and by fostering interaction between leading experts in the field and younger mathematicians (graduate students and postdocs); dissemination of knowledge in this rapidly evolving area of mathematics will be facilitated by regularly held winter and summer schools and conferences.
这个合作项目的主要目的是深入研究同调镜像对称猜想。Auroux,Katzarkov,Kontsevich,奥尔洛夫和Seidel将领导一个协调一致的努力,制定和理解同调镜像对称系统的方式,并将其扩展到一般类型的品种和非交换品种。这需要在同调代数、非交换几何和辛几何方面做一些基础工作。另一个目标是研究镜像对称在代数几何(例如研究某些代数簇的合理性)和辛拓扑(特别是拉格朗日子流形)中的经典问题中的应用。从更广泛的角度来看,该项目旨在为理论物理学的一些最新进展提供数学对应。数学所能做的贡献是证实物理直观的可靠性和一致性,并为进一步的发展奠定基础。这在物理学的发展表明存在难以通过直接实验检测的深层和复杂结构的情况下尤其重要。与此同时,这一努力将使人们有可能回答一些纯粹的数学(几何)问题,其中一些已经开放了很长一段时间。将通过定期会议和讲习班开展合作,并促进该领域领先专家与年轻数学家(研究生和博士后)之间的互动;定期举办的冬季和夏季学校和会议将促进这一快速发展的数学领域的知识传播。

项目成果

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Paul Seidel其他文献

Gamification of Science
科学游戏化
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Paul Seidel;J. Seifert;Alf Perschk
  • 通讯作者:
    Alf Perschk
Effect of Photodoping on the Fiske Resonances of YBa2Cu3Ox Grain Boundary Josephson Junctions
光电掺杂对YBa2Cu3Ox晶界约瑟夫森结费斯克共振的影响
  • DOI:
    10.1023/a:1022671615180
  • 发表时间:
    1998
  • 期刊:
  • 影响因子:
    0
  • 作者:
    M. Medici;J. Elly;M. Razani;A. Gilabert;F. Schmidl;Paul Seidel;Axel Hoffmann;I. Schuller
  • 通讯作者:
    I. Schuller
Abbreviated terminology of oligosaccharide chains. Recommendations 1980.
寡糖链的缩写术语。
Characterization of energy barrier and particle size distribution of lyophilized ferrofluids by magnetic relaxation measurements
  • DOI:
    10.1016/j.jmmm.2006.10.1187
  • 发表时间:
    2007-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Frank Schmidl;Peter Weber;Torsten Koettig;Markus Büttner;Stefan Prass;Christoph Becker;Michael Mans;Jochen Heinrich;Michael Röder;Kerstin Wagner;Dimitr V. Berkov;Peter Görnert;Gunnar Glöckl;Werner Weitschies;Paul Seidel
  • 通讯作者:
    Paul Seidel
Effects of self-assembled gold nanoparticles on YBa2Cu3O7−δ thin films and devices
自组装金纳米颗粒对 YBa2Cu3O7−δ 薄膜和器件的影响
  • DOI:
  • 发表时间:
    2012
  • 期刊:
  • 影响因子:
    0
  • 作者:
    P. Michalowski;C. Katzer;F. Schmidl;Paul Seidel
  • 通讯作者:
    Paul Seidel

Paul Seidel的其他文献

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{{ truncateString('Paul Seidel', 18)}}的其他基金

Lefschetz Fibrations, Their Noncommutative Counterparts, and Formal Groups
Lefschetz 纤维、它们的非交换对应物以及形式群
  • 批准号:
    1904997
  • 财政年份:
    2019
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Symplectic Geometry Workshop at the Isaac Newton Institute
艾萨克·牛顿研究所辛几何研讨会
  • 批准号:
    1727545
  • 财政年份:
    2017
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Lefschetz Fibrations, Mapping Tori, and Dynamics on Moduli Spaces of Objects
物体模空间上的 Lefschetz 纤维、映射环面和动力学
  • 批准号:
    1500954
  • 财政年份:
    2015
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
FRG: Collaborative Research: Wall-crossings in Geometry and Physics
FRG:合作研究:几何和物理的跨越
  • 批准号:
    1265196
  • 财政年份:
    2013
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Cohomological methods in symplectic topology
辛拓扑中的上同调方法
  • 批准号:
    1005288
  • 财政年份:
    2010
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Fukaya Categories and Applications
深谷类别和应用
  • 批准号:
    0405516
  • 财政年份:
    2004
  • 资助金额:
    --
  • 项目类别:
    Standard Grant

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