Conference on Categorical Methods in Topology and Quantum Geometry; Fall 2009, Dallas, Texas

拓扑学和量子几何分类方法会议；

• 批准号: 0936047
• 负责人: Dagan Karp
• 金额: $ 2.39万
• 依托单位: Harvey Mudd College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0936047&HistoricalAwards=false
• 关键词: Conference; Categorical; Methods; Topology; Quantum

A scientific symposium titled "Categorical Methods in Topology and Quantum Geometry" will take place at the National Meeting of the Society for Advancement of Chicano and Native Americans in Science(SACNAS) in Dallas, Texas, October 15-18, 2009. The two a priori disparate fields of low dimensional topology and quantum geometry have recently been related through the involvement of categorical methods. Exciting progress has been recently made in each of these subjects independently, including the Weinstein conjecture in dimension three and Donaldson-Thomas/Gromov-Witten duality for all toric threefolds. Important open questions motivate continued study; these include the general Weinstein conjecture, and the trilogy of equivalences between Gromov-Witten theory, Donaldson-Thomas theory and Pandharipande-Thomas theory. Central to our symposium, these fields have recently been related through their use of derived categories and categorification. This includes the categorification of Khovanov and its many generalizations, the categorification of Donaldson-Thomas theory by Behrend and Joyce-Song and the derived categories of Pandharipande- Thomas theory. In addition, the program of Cautis and Kamnitzer shows categorification results in topology may be recast in some instances as isomorphisms of derived categories in algebraic geometry. The speakers at this symposium will announce accomplishments and also discuss new directions of research. Specifically, Renzo Cavalieri will discuss derived categories in GW and DT theories, Emille Davie will discuss applications to low dimensional topology, and Juan Ortiz- Navaro will discuss categorification, Khovanov homology and its generalizations.This symposium will enable and encourage students and other scientists to pursue research in areas related to the interaction of quantum geometry and topology, provide the opportunity for scientists to interact and foster collaboration and new research, and disseminate knowledge to a wide and extraordinarily diverse audience. While the reasons for organizing a scientific symposium on topology and quantum geometry are many, there is additionally an acute need to do so for an audience of underrepresented minorities. There is at this time significant underrepresentation of minorities in the mathematical sciences; this underrepresentation is evidently severe in both topology and quantum geometry and certainly the intersection of these subjects. There are very important questions that need to be addressed in these subjects, and it is necessary to attract a broad and diverse audience to work on these problems. Gromov-Witten theory and related fields have been extremely successful in solving outstanding problems, some over 100 years old, in several branches of mathematics and physics. Low dimensional topology is not only of basic importance in geometry and topology, but in several areas of applied mathematics as well, as highlighted in this symposium. It is predicted that underrepresented minorities will become the majority of United States Citizens in the not so distant future; as such, it is in the long term interest of topology and quantum geometry to have increased participation from members of these groups. Moreover, given the importance of these subjects to mathematics and science in general, it is in our national interest to work against the underrepresentation of minorities conducting research in these fields.

一项题为“拓扑和量子几何学的分类方法”的科学研讨会将在2009年10月15日至18日在得克萨斯州达拉斯的奇卡诺和美洲原住民科学学会（SACNAS）的全国会议上举行。 最近在每个主题中都取得了令人兴奋的进步，包括第三维的韦恩斯坦猜想和所有三倍的三倍的唐纳德森 - 托马斯/格罗莫夫二重性。 重要的开放问题激励继续学习；其中包括一般的韦恩斯坦猜想，以及格罗莫夫·韦特理论，唐纳森·托马斯理论和潘达里蒂普德·托马斯理论之间的等价三部曲。这些领域最近通过使用衍生类别和分类而与这些领域有关。 这包括对Khovanov的分类及其许多概括，Behrend和Joyce-Song对Donaldson-Thomas理论的分类以及Pandharipande-Thomas理论的派生类别。此外，在某些情况下，CAUTIS和KAMNITZER的程序在拓扑结构中显示出拓扑的分类结果，可能是代数几何形状中派生类别的同构。该研讨会上的演讲者将宣布成就，并讨论新的研究方向。 Specifically, Renzo Cavalieri will discuss derived categories in GW and DT theories, Emille Davie will discuss applications to low dimensional topology, and Juan Ortiz- Navaro will discuss categorification, Khovanov homology and its generalizations.This symposium will enable and encourage students and other scientists to pursue research in areas related to the interaction of quantum geometry and topology, provide the opportunity for scientists to interact and foster协作和新研究，并将知识传播给广泛而多样的受众。虽然组织拓扑和量子几何学的科学症结研讨会的原因很​​多，但对于代表人数不足的少数群体的观众来说，急需这样做。目前有数学科学中少数群体的代表性不足；在拓扑和量子几何学上，这种代表性不足显然是严重的，当然也是这些受试者的交集。这些主题中需要解决一些非常重要的问题，有必要吸引广泛而多样的受众来解决这些问题。在数学和物理学的几个分支机构中，Gromov-Witten的理论和相关领域在解决了一些超过100年的杰出问题方面非常成功。低维拓扑不仅在几何学和拓扑中具有基本重要性，而且在本次研讨会中强调的几个应用数学领域也是如此。据预测，在不远的未来，代表性不足的少数群体将成为大多数美国公民。因此，这些群体成员的参与增加是拓扑和量子几何形状的长期利益。此外，鉴于这些受试者对数学和科学的重要性，我们的国家利益符合我们的国家利益，反对在这些＆＃64257; elds中进行研究的代表性不足。