Conference Proposal - Structure of 3-manifold Groups

会议提案 - 3流形组的结构

• 批准号: 1747833
• 负责人: Genevieve Walsh
• 金额: $ 2.7万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-01-01 至 2022-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1747833&HistoricalAwards=false
• 关键词: Conference; Proposal; Structure; manifold; Groups

The conference, "Structure of 3-manifold groups" will be held in Marseille, Luminy (France) at the Centre International de Rencontres Mathematiques (CIRM) from February 26 to March 2, 2018. The organizers expect that the meeting will have about 90 participants. The award funds participation of US based mathematicians in this event. The topics covered at the conference are of high current interest with difficult outstanding problems. There have recently been new techniques developed regarding this family of problems and related conjectures regarding the structure of 3-manifold groups. The organizers expect that bringing mathematicians together from different areas with different points of view regarding these topics will serve mathematical progress. This conference is part of a semester whose aim is to foster international collaboration, particularly between the United States and France. There is time allowed for interaction and collaboration, and the mix of senior and junior mathematicians should be very productive.The conference will focus on determining which groups are the fundamental groups of 3-manifolds. Understanding which groups are 3-manifold groups is a very old problem, but there are new ways of thinking about groups that allow to make progress in certain cases. In particular, much progress has been made in the field of relatively hyperbolic groups, and specific classes of hyperbolic groups, such as free-by-cyclic groups. Specifically, the conference will cover topics about Poincare duality groups, when certain classes of groups are the fundamental groups of 3-manifolds, pro-finite completions of groups, surface subgroups of groups, and decompositions of groups analogous to decompositions of 3-manifolds. The main goal is that specific results will be obtained by bringing individuals together. There is a continuously evolving website for the meeting at https://walsh-paoluzzi.weebly.com/conference.html. In particular, interested participants can pre-register at that site.

会议“ 3-manifold小组的结构”将于2018年2月26日至3月2日在国际de Rencontres Mathematiques（CIRM）的Marseille举行，2018年3月2日至2018年3月2日。该奖项资金基金的数学家参与了这一事件。会议上涵盖的主题具有很高的兴趣，遇到了困难的问题。最近，关于这个问题和相关的猜想，已经开发了有关3个manifold群体的结构的新技术。组织者期望将数学家从不同领域的不同领域聚集在一起，这些观点对这些主题有不同的观点将有助于数学进步。这次会议是一个学期的一部分，其目的是促进国际合作，尤其是在美国和法国之间。有时间进行互动和协作，高级和初级数学家的组合应该非常有生产力。会议将集中精力确定哪些群体是3个Manifolds的基本群体。了解哪些小组是三个manifold群体是一个非常古老的问题，但是有一些新的思考群体在某些情况下可以取得进展的新方法。 特别是，在相对双曲线组和特定的双曲线组（例如自由循环基团）的领域已经取得了很多进展。具体而言，当某些类别的组是3个manifolds的基本组，组的群体，组的表面亚组和类似于3个曼物的分解的组的分解时，会议将涵盖有关庞加罗二元性群体的主题。 主要目标是通过将个人聚集在一起来获得特定的结果。 会议上有一个不断发展的网站，网址为https://walsh-paoluzzi.weebly.com/conference.html。特别是，有兴趣的参与者可以在该站点进行预注册。