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

2007年10月12日，一场名为“低维拓扑和量子几何”的科学研讨会将在密苏里州堪萨斯城举行的奇卡诺人和美洲原住民科学进步协会（SACNAS）全国会议上举行。低维拓扑学和量子几何这两个先天不同的领域通过理论物理和弦理论联系在一起。最近，这些学科都取得了令人兴奋的进展，包括三维温斯坦猜想的证明，以及0度Donaldson-Thomas/Gromov-Witten对偶。重要的开放性猜想激励着继续研究；这些猜想不仅包括高阶的Gromov-Witten/Donaldson-Thomas猜想和一般的Weinstein猜想，还包括体积猜想、蠕变分解猜想等重要课题。此外，我们研讨会的核心，是关于这两个主题的重要猜想。最值得注意的是大N对偶性，将Gromov-Witten理论与结理论和低维拓扑联系起来。本次研讨会的演讲者将宣布研究成果并讨论新的研究方向。具体来说，Joel Kamnitzer将介绍结理论及其与派生范畴的关系，Mariel vazqueuz将讨论结理论的应用，Kevin Costello将讨论与代数几何和Gromov-Witten理论的联系。本次研讨会将使并鼓励学生和其他科学家在量子几何和低维拓扑相互作用的相关领域进行研究，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。虽然组织关于低维拓扑和量子几何的科学研讨会的原因有很多，但对于代表性不足的少数群体的听众来说，这样做的迫切需要。目前，少数民族在数学科学领域的代表性明显不足；这种代表性不足在低维拓扑和量子几何以及这些学科的交叉领域都很严重。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研究这些问题。Gromov-Witten理论及相关理论&amp；#64257；在数学和物理的几个分支中，科学家们在解决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和拓扑中具有基本的重要性，而且在应用数学的几个领域中也具有重要意义，正如本次研讨会所强调的那样。据预测，未被充分代表的少数民族将成为美国公民的大多数；因此，增加这些小组成员的参与是对低维拓扑和量子几何的长期兴趣。此外，考虑到这些学科对数学和科学的重要性，反对少数民族在这些领域进行研究的代表性不足符合我们的国家利益。本次研讨会已由SACNAS批准并安排。关于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。

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.