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.

组委会由 Vincent Bouchard（阿尔伯塔大学）、Tom Coates（伦敦帝国理工学院）、Emma Previato（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）组成作为主席，将在 10 月的一周内在班夫国际研究站组织为期 5 天的研讨会，题为“卡拉比-丘空间的新递归公式和可积性” 2011 年 16-21 日 (http://www.birs.ca/events/2011/5-day-workshops/11w5114)。计划中的研讨会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。主要目标是为 2007 年物理学家 Eynard 和 Orantin 在随机矩阵研究中新发现的拓扑递归公式及其由弦理论家 Marino 和 Bouchard-Klemm-Marino 实现的 Gromov-Witten 理论实现建立拓扑和几何基础-Pasquetti。该领域的主要问题之一是由它们引起的重塑猜想。它指出，任意复曲面 Calabi-Yau 3 重的开和闭 Gromov-Witten 不变量都是通过基于镜像曲线的复分析的 Eynard-Orantin 拓扑递归计算出来的，这非常神奇。研讨会的很大一部分时间将致力于解决这个尚未解决的猜想。研讨会的另一个重点是发现卡拉比-丘空间的格罗莫夫-维滕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。计划中的研讨会的主题是第一个全面的国际研讨会专门致力于上述主题，不适合单一的数学学科。研讨会的一个重要方面是其数学和理论物理不同领域交叉融合的功能。主题的起源是随机矩阵统计研究的土壤。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。该理论本身涵盖了很大的数学领域。迄今为止，严格建立的理论示例范围从双曲几何到代数几何，再到拓扑图论的组合数学。这些严格理论的数学工具是拉普拉斯变换和经典复分析。对所提出主题的任何新理解都有望增强我们当前对镜像对称、格罗莫夫-维滕理论和某些组合问题的了解。 BIRS 研讨会计划吸引广泛的研究人员，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。由于该学科的主要参与者是早期职业生涯的博士后研究人员和教员，因此研讨会预计会引起许多研究生和博士后学者的关注。