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-流形的拓扑和几何透视国际会议将于2016年6月5日至10日在克罗地亚杜布罗夫尼克的大学间中心举行。本次会议将汇集来自世界各地的四维拓扑和几何领域的领先研究人员和新兴数学家，旨在为该主题的开放问题的未来研究提供方向，并将年轻的数学家引入该领域。NSF的资金将用于支付美国参与者的差旅和住宿费用，优先考虑受邀演讲者，以及没有其他资金来源的初级数学家。会议将产生的影响，在促进沟通和拓扑学家之间的合作在不同的职业阶段，提供观点和新的研究方向，为年轻的数学家。现代4-流形理论可以说已经开始在20世纪80年代初的工作唐纳森应用规范理论。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Floer理论不变量已经取得了显着的进展。然而，一些最引人注目的应用程序的这些不变量的3流形，并从某种角度来看，哲学动机的不变量本身，涉及到4流形直接或通过所涉及的技术。此外，在四维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根植于弗洛尔理论的新思想。会议将起到宣传这些未解决问题的最新思想和方法的双重作用，并向年轻一代介绍4-流形理论。随着一些杰出的领导人在该领域的参与，以及许多有才华的年轻数学家，组织者希望这次会议将触发新的活动和进展，在4-流形拓扑。作为会议的一部分，我们还计划庆祝罗恩·芬图谢尔和罗恩·斯特恩的工作，他们对该领域的发展非常有影响力。 组织者将编辑和出版一卷与这次会议有关的会议记录，其中有许多发言者的贡献。该卷的核心部分将致力于基于Rob Kirby，罗恩Fintushel和罗恩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。https://www.renyi.hu/~ldtbud/Dubrovnik/