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-manifolds拓扑和几何学观点的国际会议将于2016年6月5日至10日在克罗地亚杜布罗夫尼克的国际大学中心举行。这次会议将汇集领先的研究人员和新兴的数学家在世界各地的4维拓扑和几何学中，目的是为未来的研究中有关该主题开放问题的研究提供指导，并将年轻的数学家介绍给该领域。 NSF资金将用于支付美国参与者的旅行和住宿费用，并优先考虑受邀演讲者，而没有其他资金来源的初级数学家则优先。该会议将对在各个职业阶段促进拓扑师之间的沟通和协作产生影响，为年轻的数学家提供观点和新的研究指示。可以说，现代的4个模型理论始于1980年代初，唐纳森（Donaldson）的工作采用了仪表理论。自2000年以来，许多低维拓扑师的注意力已转移到Dimension 3，在该维度3中，浮动理论不变性允许了显着的进步。但是，这些3个manifolds的这些不变的最引人注目的应用，从某个角度来看，不变的人本身的哲学动机与4个模型直接或通过所涉及的技术有关。此外，在4个manifold理论中存在许多基本的未解决的问题，这些问题可能会产生植根于浮子理论的新思想。该会议将发挥两性功能，以宣传这些未解决的问题的最新想法和方法，并将年轻一代引入4-manifold理论。随着该领域的一些杰出领导人以及许多才华横溢的年轻数学家的参与，组织者希望这次会议能够解决4-Manifold拓扑的新活动和进步。作为会议的一部分，我们还计划庆祝Ron Fintushel和Ron Stern的作品，这在该领域的发展中非常有影响力。 组织者将在许多演讲者的贡献中编辑和发布与本次会议相关的诉讼程序。该卷的核心将是一个专门针对4个manifold拓扑问题的部分，该部分基于Rob Kirby，Ron Fintushel和Ron Stern.further在会议期间在会议期间运行的问题会话，可以在会议网页上找到，https://wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww.hu/thu/thu/thu/thu/thu/tlowdubrovnik/dubrovnik/dubrovnik/dubrovnik/dubrovnik/dubrovnik/