IHES summer school on Moduli Problems in Symplectic Geometry

IHES 辛几何模问题暑期学校

• 批准号: 1510109
• 负责人: Michael Hutchings
• 金额: $ 2.67万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-03-01 至 2016-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1510109&HistoricalAwards=false
• 关键词: IHES; summer; Moduli; Problems; Symplectic

The conference entitled "Summer School on Moduli Problems in Symplectic Geometry" will take place at the IHES (Institute des Hautes Etudes Scientifiques) in Bures-sur-Yvette, France from July 6-17, 2015. The conference website is located at https://indico.math.cnrs.fr/conferenceDisplay.py?confId=585. This conference will provide PhD students, postdocs, and young researchers with an overview of the most recent technology in symplectic geometry, as well as faciliate collaborations to further develop this technology. This grant will provide travel funding for young US researchers lacking other federal support, with an emphasis on members of underrepresented groups, to attend this conference. This will enable the next generation of US researchers to keep up with the latest developments and stay at the forefront of symplectic geometry.Symplectic geometry has made enormous advances since the introduction of (pseudo)holomorphic curves by Gromov in 1985. However in order to use holomorphic curves in symplectic geometry, a substantial amount of analysis is needed to regularize the moduli spaces of holomorphic curves. In the 80's and 90's these moduli spaces were regularized using geometric perturbation techniques. However since then, symplectic geometry has moved beyond the scope of problems to which geometric perturbation techniques are applicable, leaving a serious gap in the foundations of the subject. Perhaps the most successful and promising technology for filling this gap is the polyfold theory of Hofer, Wysocki and Zehnder. The conference has two main goals. The first goal is to educate a large audience in polyfold theory, in order to enable more researchers to begin developing and using these new techniques. The second goal is to connect the abstract perturbations of polyfolds to the classical geometric perturbations in order to facilitate computations of invariants.

题为“辛几何中的模问题暑期学校”的会议将于2015年7月6日至17日在法国布雷斯-苏尔-伊维特的IHES（高等科学研究所）举行。会议网站位于https://indico.math.cnrs.fr/conferenceDisplay.py? confId=585。本次会议将为博士生，博士后和年轻的研究人员提供辛几何最新技术的概述，以及促进合作，以进一步发展这项技术。这笔赠款将为缺乏其他联邦支持的年轻美国研究人员提供旅费，重点是代表性不足的群体的成员参加这次会议。这将使美国的下一代研究人员能够跟上最新的发展，并保持在辛几何的最前沿。自1985年Gromov引入（伪）全纯曲线以来，辛几何已经取得了巨大的进步。然而，为了在辛几何中使用全纯曲线，需要大量的分析来正则化全纯曲线的模空间。在80年代和90年代，这些模空间使用几何扰动技术进行正则化。然而，从那时起，辛几何已经超出了几何摄动技术适用的问题的范围，留下了严重的差距的基础上的问题。也许填补这一空白的最成功和最有前途的技术是霍费尔，Wysocki和Zehnder的多重折叠理论。会议有两个主要目标。第一个目标是在多重折叠理论中教育大量的观众，以便使更多的研究人员开始开发和使用这些新技术。第二个目标是连接抽象的扰动的多重折叠的经典几何扰动，以方便计算的不变量。