Conference on Low Dimensional Topology and Quantum Geometry, Kansas City, MO

低维拓扑和量子几何会议，密苏里州堪萨斯城

• 批准号: 0752978
• 负责人: Alan Weinstein
• 金额: $ 0.44万
• 依托单位: University of California-Berkeley
• 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: 2007-12-01 至 2008-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0752978&HistoricalAwards=false
• 关键词: Conference; Low; Dimensional; Topology; Quantum

A scientific symposium titled Low Dimensional Topology and Quantum Geometry will take place at the National Meeting of the Society for the Advancement of Chicano and Native Americans in the Sciences (SACNAS) in Kansas City, Missouri on October 12, 2007. The two a priori disparate fields of low dimensional topology and quantum geometry are related through theoretical physics and string theory. Exciting progress has recently been made in each of these subjects independently, including a proof of the Weinstein conjecture in dimension three, and the degree-0 Donaldson-Thomas/Gromov-Witten duality. Important open conjectures motivate continued study; these include notonly the higher-degree Gromov-Witten/Donaldson-Thomas conjecture and the general Weinstein conjecture, but also such important topics as the Volume conjecture, the Crepant Resolution Conjecture. Furthermore, and central to our symposium, there are important conjectures relating these two sub jects. Most notable is Large N duality, relating Gromov-Witten theory to knot theory and low dimensional topology. The speakers at this symposium will announce accomplishments and also discuss new directions of research. Specifically, Joel Kamnitzer will give an introduction to knot theory and its relation to derived categories, Mariel Vazqeuz will discuss applications of knot theory, and Kevin Costello will discuss connections to Algebraic Geometry and Gromov-Witten theory. This symposium will enable and encourage students and other scientists to pursue research in areas related to the interaction of quantum geometry and low dimensional 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 low dimensional 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 low dimensional 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; as such, it is in the long term interest of low dimensional topology and quantum geometry to have increased participation from members of these groups. Moreover, given the importance of these sub jects to mathematics and science in general, it is in our National interest to work against the underrepresentation of minorities conducting research in these fields. This symposium has been approved and scheduled by SACNAS. Further information about mathematics at SACNAS in general, and about this symposium in particular, can be found, respectively, at http://www.uprh.edu/~sacnas/ and http://math.berkeley.edu/~dkarp/sacnas/2007.html.

2007年10月12日，在密苏里州堪萨斯城举行的墨西哥裔美国人和美洲原住民科学促进会（SACNAS）全国会议上，将举行一个题为“低维拓扑和量子几何”的科学研讨会。低维拓扑学和量子几何学这两个先验不同的领域通过理论物理学和弦理论联系起来。最近在这些学科中的每一个都取得了令人兴奋的进展，包括在三维中证明温斯坦猜想，以及0度Donaldson-Thomas/Gromov-Witten对偶。重要的开放性猜想激发了人们对它的持续研究;这些猜想不仅包括高次Gromov-Witten/Donaldson-Thomas猜想和一般的Weinstein猜想，还包括诸如体积猜想、Crepant归结猜想等重要课题。此外，也是我们讨论会的中心，有一些与这两个主题相关的重要文献。最值得注意的是大N对偶，将Gromov-Witten理论与纽结理论和低维拓扑联系起来。本次研讨会的演讲者将宣布成就，并讨论新的研究方向。具体来说，乔尔卡姆尼策将介绍纽结理论及其与派生类别的关系，玛丽埃尔瓦兹奎兹将讨论纽结理论的应用，凯文科斯特洛将讨论代数几何和格罗莫夫-威滕理论的联系。本次研讨会将使并鼓励学生和其他科学家在与量子几何和低维拓扑的相互作用相关的领域进行研究，为科学家提供互动和促进合作和新研究的机会，并向广泛和非常多样化的受众传播知识。虽然组织一个关于低维拓扑和量子几何的科学研讨会的原因有很多，但也迫切需要为代表性不足的少数群体听众这样做。有在这个时候显着代表性不足的少数民族在数学科学;这种代表性不足显然是严重的低维拓扑和量子几何，当然这些学科的交叉。在这些主题中有一些非常重要的问题需要解决，有必要吸引广泛和不同的受众来解决这些问题。Gromov-Witten理论和相关的ELDs在解决数学和物理学的几个分支中的突出问题方面非常成功，有些问题已经有100多年的历史了。低维拓扑不仅在几何学和拓扑学中具有基本的重要性，而且在应用数学的几个领域也具有重要意义，正如本次研讨会所强调的那样。据预测，代表性不足的少数群体将成为美国公民的大多数;因此，增加这些群体成员的参与符合低维拓扑和量子几何的长期利益。此外，考虑到这些学科对数学和科学的重要性，我们的国家利益是努力解决少数民族在这些领域进行研究的代表性不足的问题。本次研讨会已得到SACNAS的批准和安排。有关SACNAS数学的更多信息，特别是关于这次研讨会的信息，可以分别在http://www.uprh.edu/~sacnas/和http://math.berkeley.edu/~dkarp/sacnas/2007.html上找到。