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“Structure of 3-manifold Group”将于2018年2月26日至3月2日在法国卢米尼马赛的国际数学竞赛中心（CIRM）举行。组织者预计会议将有约90人参加参与者。该奖项资助美国数学家参与本次活动。会议讨论的议题是当前热点问题、突出问题。最近针对这一系列问题和有关 3 流形群结构的相关猜想开发了新技术。组织者希望将来自不同领域、对这些主题持有不同观点的数学家聚集在一起，将有助于数学的进步。这次会议是一个学期的一部分，其目的是促进国际合作，特别是美国和法国之间的合作。有时间进行互动和协作，高级和初级数学家的混合应该非常富有成效。会议将集中于确定哪些群是 3-流形的基本群。理解哪些群是三流形群是一个非常老的问题，但是有一些新的思考群的方法可以在某些情况下取得进展。 特别是，在相对双曲群和特定类别的双曲群（例如自由循环群）领域取得了很大进展。具体来说，会议将涵盖有关庞加莱对偶群的主题，其中某些群是 3-流形的基本群、群的临有限完备性、群的表面子群以及类似于 3-流形分解的群分解。 主要目标是通过将个人聚集在一起来获得具体结果。 该会议有一个不断发展的网站：https://walsh-paoluzzi.weebly.com/conference.html。特别是，有兴趣的参与者可以在该网站进行预先注册。