New Recursion Formulae and Integrability for Calabi-Yau Spaces

Calabi-Yau 空间的新递归公式和可积性

• 批准号: 1104751
• 负责人: Motohico Mulase
• 金额: $ 1万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1104751&HistoricalAwards=false
• 关键词: New; Recursion; Formulae; Integrability; Calabi

The organizing committee, consisting of Vincent Bouchard (University of Alberta), Tom Coates (Imperial College, London), Emma Previato (Boston University), Jian Zhou (Tsinghua University, Beijing), and Motohico Mulase (University of California, Davis) serving as chair, will organize a 5-day workshop titled "New Recursion Formulae and Integrablity for Calabi-Yau Spaces" at the Banff International Research Station during the week of October 16-21, 2011 (http://www.birs.ca/events/2011/5-day-workshops/11w5114). The planned workshop has a clear set of focused goals, and is unique among conferences in related subjects. The main objective is to establish a topological and geometric foundation of a newly discovered topological recursion formula of 2007 by physicists Eynard and Orantin in their work on random matrices, and its Gromov-Witten theoretic realization due to string theorists Marino and Bouchard-Klemm-Marino-Pasquetti.One of the major problems in this area is the Remodeling Conjecture due to them. It states that both open and closed Gromov-Witten invariants of an arbitrary toric Calabi-Yau 3-fold are, quite miraculously, calculated by the Eynard-Orantin topological recursion based on the complex analysis of the mirror curve. A good part of the workshop will be devoted to attacking this unsolved conjecture. Another emphasis of the workshop is placed on discovering yet unknown relation between the generating function of Gromov-Witten invariants of Calabi-Yau spaces and integrable nonlinear partial differential equations.The subject matter of the planned Workshop, which is the first full-scale international workshop specifically devoted to the topics mentioned above, does not fit in a single discipline of mathematics. An important aspect of the Workshop is its function of cross fertilization of different areas of mathematics and theoretical physics. The origin of the main topic is in the soil of statistical study of random matrices. It's geometric significance was discovered by string theorists. It's mathematical nature apparently lies in topology. The theory itself covers a large area of mathematics. So far rigorously established examples of the theory range from hyperbolic geometry to algebraic geometry and to combinatorics of topological graph theory. The mathematical apparatus of these rigorous theories is the Laplace transform and classical complex analysis. Any new understanding of the proposed topics is expected to enhance our current knowledge of mirror symmetry, Gromov-Witten theory, and certain combinatorial problems. The BIRS Workshop plans to bring a wide variety of researchers, to nurture international and interdisciplinary collaborations among young participants, and to generate a larger momentum in the discipline. Since the key players of the subjects are postdoctoral researchers and faculty members in their early careers, the Workshop is expected draw the attention of many graduate students and postdoctoral scholars.

组织委员会，由文森特·布沙尔（阿尔伯塔大学），汤姆科茨（帝国理工学院，伦敦），艾玛·普雷维亚托（波士顿大学），Jian Zhou（清华大学，北京），和Motohico Mulase（加州大学戴维斯分校）担任主席，将组织为期5天的研讨会，题为“新的递归公式和Calabi-Yau空间的可积性”2011年10月16日至21日的一周期间在班夫国际研究站（http：//www.birs.ca/events/2011/5-day-workshops/11w5114）。计划中的讲习班有一套明确的重点目标，在相关主题的会议中是独一无二的。主要目的是为物理学家Eynard和Orantin在2007年关于随机矩阵的工作中新发现的拓扑递归公式以及弦理论家Marino和Bouchard-Klemm-Marino-Pasquetti的Gromov-Witten理论实现建立拓扑和几何基础，这一领域的主要问题之一是由他们提出的重塑猜想。它指出，开放和封闭的Gromov-Witten不变量的任意环面Calabi-Yau 3倍，相当神奇地，计算的Eynard-Orantin拓扑递归的基础上复分析的镜像曲线。研讨会的很大一部分将致力于解决这个悬而未决的猜想。研讨会的另一个重点是发现Calabi-Yau空间的Gromov-Witten不变量的生成函数与可积非线性偏微分方程之间的未知关系。计划中的研讨会是第一个专门致力于上述主题的全面国际研讨会，其主题不适合于单一的数学学科。讲习班的一个重要方面是它在数学和理论物理的不同领域的交叉施肥的功能。主要课题的起源是在随机矩阵统计研究的土壤中。它的几何意义是由弦理论家发现的。它的数学本质显然在于拓扑学。这个理论本身涵盖了一个很大的数学领域。到目前为止，严格建立的例子，理论范围从双曲几何代数几何和组合的拓扑图论。这些严格理论的数学工具是拉普拉斯变换和经典复分析。任何新的理解所提出的主题，预计将提高我们目前的知识镜像对称，Gromov-Witten理论，和某些组合问题。BIRS研讨会计划带来各种各样的研究人员，培养年轻参与者之间的国际和跨学科合作，并在该学科中产生更大的动力。由于该主题的主要参与者是博士后研究人员和教师在他们的早期职业生涯，讲习班预计将吸引许多研究生和博士后学者的注意。