Perspectives in topology and geometry of 4-manifolds

4 流形的拓扑和几何视角

• 批准号: 1612071
• 负责人: Gordana Matic
• 金额: $ 4.61万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-05-15 至 2019-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1612071&HistoricalAwards=false
• 关键词: Perspectives; topology; geometry; manifolds

The international conference on Perspectives in Topology and Geometry of 4-manifolds will be held June 5--10, 2016 at the Inter University Centre in Dubrovnik, Croatia. This conference will bring together leading researchers and emerging mathematicians in 4-dimensional topology and geometry from around the world, with the aims of providing directions for future research on open problems in the subject and introducing younger mathematicians to the field. NSF funds will be used to defray travel and lodging expenses for participants based in the US, with priority for invited speakers, and for junior mathematicians without other sources of funding. The conference will have an impact in fostering communication and collaboration between topologists at various career stages, providing perspective and new research directions for young mathematicians. Modern 4-manifold theory can be said to have begun in the early 1980s with the work of Donaldson applying gauge theory. Since 2000, the attention of many low-dimensional topologists has shifted to dimension 3, where Floer-theoretic invariants have allowed remarkable progress. However, some of the most striking applications of these invariants of 3-manifolds, and from a certain point of view the philosophical motivation for the invariants themselves, relate to 4-manifolds either directly or through the techniques involved. Moreover, there are a number of fundamental unsolved problems in 4-manifold theory that may yield to new ideas rooted in Floer theory. The conference will serve the dual function of publicizing the newest ideas and approaches to these unsolved problems, and of introducing a younger generation to 4-manifold theory. With participation by some of the preeminent leaders in the field as well as many talented younger mathematicians, the organizers hope that this conference will touch off new activity and progress in 4-manifold topology. As a part of the conference we also plan to celebrate the work of Ron Fintushel and Ron Stern which has been very influential in the development of the field. The organizers will edit and publish a volume of proceedings associated with this conference, with contributions from many of the speakers. The centerpiece of the volume will be a section devoted to open problems in 4-manifold topology based on problem sessions run during the conference by Rob Kirby, Ron Fintushel and Ron Stern.Further details can be found on the conference webpage, https://www.renyi.hu/~ldtbud/Dubrovnik/

4流形拓扑与几何展望国际会议将于2016年6月5日至10日在克罗地亚杜布罗夫尼克国际大学中心举行。本次会议将汇集来自世界各地的四维拓扑和几何领域的主要研究人员和新兴数学家，旨在为该学科的开放性问题的未来研究提供方向，并将年轻数学家引入该领域。NSF资金将用于支付美国参与者的旅行和住宿费用，优先考虑受邀演讲者和没有其他资金来源的初级数学家。会议将促进各职业阶段拓扑学家之间的交流与合作，为年轻数学家提供新的研究视角和方向。现代四流形理论可以说是从20世纪80年代初唐纳森应用规范理论开始的。自2000年以来，许多低维拓扑学家的注意力已经转移到3维，其中花理论不变量已经取得了显著的进展。然而，3流形的这些不变量的一些最引人注目的应用，以及从某种角度来看，不变量本身的哲学动机，直接或通过所涉及的技术与4流形相关。此外，在四流形理论中还有一些基本的未解决的问题，这些问题可能会产生植根于弗洛尔理论的新思想。这次会议将起到双重作用，一是宣传解决这些未解决问题的最新思想和方法，二是向年轻一代介绍四流形理论。在一些杰出的领域领导者以及许多有才华的年轻数学家的参与下，组织者希望这次会议将在4流形拓扑方面开启新的活动和进展。作为会议的一部分，我们还计划庆祝Ron Fintushel和Ron Stern的工作，他们在该领域的发展中非常有影响力。组织者将编辑和出版与本次会议有关的论文集，其中包括许多发言者的贡献。该卷的核心部分将是一个章节，专门讨论基于Rob Kirby， Ron Fintushel和Ron Stern在会议期间运行的问题会话的4流形拓扑中的开放问题。详情可浏览会议网页https://www.renyi.hu/~ldtbud/Dubrovnik/