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

一个题为“拓扑学和量子几何学中的分类方法”的科学研讨会将于2009年10月15日至18日在德克萨斯州达拉斯举行的墨西哥裔美国人和美洲原住民科学促进协会全国会议上举行。低维拓扑学和量子几何学这两个先验的不同领域最近通过范畴方法的介入而联系起来。 最近在这些主题中的每一个都取得了令人兴奋的进展，包括三维的Weinstein猜想和所有Toric三重的Donaldson-Thomas/Gromov-Witten对偶。 重要的开放性问题激发了持续的研究;这些包括一般的温斯坦猜想，以及格罗莫夫-威滕理论，唐纳森-托马斯理论和潘达里潘德-托马斯理论之间的等价性三部曲。作为我们专题讨论会的中心，这些领域最近通过使用派生的范畴和分类而被联系起来。 这包括Khovanov的范畴化及其许多推广，Behrend和Joyce-Song对Donaldson-托马斯理论的范畴化以及Pandharipande-托马斯理论的派生范畴。此外，Cautis和Kamnitzer的程序表明，拓扑中的范畴化结果在某些情况下可以被改写为代数几何中导出范畴的同构。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，Renzo Cavalieri将讨论GW和DT理论中的派生类别，Emille Davie将讨论低维拓扑的应用，Juan Ortiz- Navaro将讨论分类，Khovanov同调及其推广。本次研讨会将使学生和其他科学家能够并鼓励他们在量子几何和拓扑的相互作用相关领域进行研究，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。虽然组织一个科学的原因fi c关于拓扑学和量子几何学的专题讨论会很多，另外迫切需要为代表人数不足的少数群体听众这样做。在这个时候有一个信号fi不能代表少数民族在数学科学;这种代表性不足显然是严重的拓扑学和量子几何学，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理论和相关领域在解决数学和物理学的几个分支中的突出问题方面取得了极大的成功，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，在不久的将来，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拓扑学和量子几何学的长期利益。此外，考虑到这些学科对数学和科学的重要性，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符合我们的国家利益。

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.