Conference on Geometry and Theoretical Physics

摘要：2006年10月27日，美国奇卡诺和美洲原住民科学促进会（SACNAS）将在佛罗里达州坦帕市召开一场名为“几何与理论物理”的科学研讨会。镜像对称、量子上同调和格罗莫夫-威滕理论是当代几何和理论物理学交叉的核心。最近，我们对这些问题的理解已经取得了很大的进步，包括完全确定了局部曲线的格罗莫夫-威腾理论（和唐纳森-托马斯理论）和环面卡拉比-丘三倍，以及威腾猜想的新证明；公布的结果包括计算某些具有基本重要性的希尔伯特方案的量子上同调，以及构造等变顶点，从而确定了所有环三倍的Gromov-Witten理论。一些重要的猜想推动了这个领域的发展，包括陈-西蒙斯/格罗莫夫-威滕对偶，唐纳森-托马斯/格罗莫夫-威滕对应，以及克雷潘分辨率猜想。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，Jim Bryan将讨论拓扑量子场论，Robin Wilson将讨论结和三流形，Vincent Bouchard将讨论粒子物理的标准模型及其与几何的关系。本次研讨会将鼓励学生和其他科学家在理论物理和数学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。虽然组织一次关于几何和理论物理的科学研讨会的原因有很多，但也有一个迫切的需要，即为那些未被充分代表的少数群体的听众这样做。目前，少数民族在数学科学领域的代表性明显不足；在格罗莫夫-维滕理论和其他与几何和物理相互作用有关的领域中，这种表述不足显然是严重的。Gromov-Witten理论中有一些非常重要的问题需要解决，有必要吸引广泛而多样化的受众来研究这些问题。格罗莫夫-威滕理论及其相关领域在解决数学和物理的几个分支的突出问题方面取得了极大的成功，其中一些问题已有100多年的历史。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，增加这些团体成员的参与符合几何和物理的长期利益。此外，考虑到几何和理论物理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。此外，还从SACNAS获得资金，用于支付演讲者和组织者的差旅费、住宿费和会议注册费。本提案中要求的资金将用于学生支持。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上找到。

AbstractAward: DMS-0640282Principal Investigator: Alan D. WeinsteinA scientific symposium titled "Geometry and Theoretical Physics"will take place at the National Meeting of the Society for theAdvancement of Chicano and Native Americans in the Sciences(SACNAS) in Tampa, Florida on October 27, 2006. Mirror Symmetry,Quantum Cohomology and Gromov-Witten theory lie at the heart ofthe intersection of contemporary geometry and theoreticalphysics. Great strides have recently been made in ourunderstanding of these subjects, including a completedetermination of the Gromov-Witten theory (and Donaldson-Thomastheory) of local curves, and of toric Calabi-Yau threefolds, andnew proofs of Witten's conjecture; announced results include thecomputation of the quantum cohomology of certain Hilbert schemesof basic importance, and a construction of the EquivariantVertex, determining the Gromov-Witten theory of all toricthreefolds. A number of important conjectures drive the field,including Chern-Simons/Gromov-Witten duality, theDonaldson-Thomas/Gromov-Witten correspondence, and the CrepantResolution Conjecture. The speakers at this symposium willannounce accomplishments and also discuss new directions ofresearch. Specifically, Jim Bryan will discuss TopologicalQuantum Field Theories, Robin Wilson will discuss knots andthree-manifolds, and Vincent Bouchard will discuss the StandardModel of particle physics, and its relation to geometry.This symposium will enable and encourage students and otherscientists to pursue research in areas related to the interactionof theoretical physics and mathematics, provide the opportunityfor scientists to interact and foster collaboration and newresearch, and disseminate knowledge to a wide and extraordinarilydiverse audience. While the reasons for organizing a scientificsymposium on geometry and theoretical physics are many, there isadditionally an acute need to do so for an audience ofunderrepresented minorities. There is at this time significantunderrepresentation of minorities in the mathematical sciences;this underrepresentation is evidently severe in Gromov-Wittentheory and other fields relating to the interactions of geometryand physics. There are very important questions that need to beaddressed in Gromov-Witten theory, and it is necessary to attracta broad and diverse audience to work on theseproblems. Gromov-Witten theory and related fields have beenextremely successful in solving outstanding problems, some over100 years old, in several branches of mathematics and physics. Itis predicted that underrepresented minorities will become themajority of United States Citizens; as such, it is in the longterm interest of geometry and physics to have increasedparticipation from members of these groups. Moreover, given theimportance of geometry and theoretical physics to mathematics andscience in general, it is in our National interest to workagainst the underrepresentation of minorities conducting researchin these fields. This symposium has been approved and scheduledby SACNAS. In addition, funding has been secured from SACNAS tocover the speakers' and organizers' travel, lodging andconference registration fees. The funding requested in thisproposal will be used for student support.Further information about mathematics at SACNAS in general, andabout this symposium in particular, can be found, respectively,at http://www.uprh.edu/~sacnas/ andhttp://math.berkeley.edu/~dkarp/sacnas.