Conference Proposal - Structure of 3-manifold Groups

“3流形群的结构”会议将于2018年2月26日至3月2日在法国马赛国际Rencontres Mathematiques中心（CIRM）举行。组织者预计会议将有大约90名与会者。该奖项资助美国数学家参加这一活动。会议所讨论的议题都是当前高度关注的、难点突出的问题。最近，关于这类问题和关于3流形群结构的相关猜想，出现了一些新的技术。组织者希望将不同领域的数学家聚集在一起，就这些主题提出不同的观点，这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。有时间进行互动和合作，高级和初级数学家的组合应该是非常富有成效的。会议将集中讨论确定哪些群是3-流形的基本群。了解哪些组是3-manifold group是一个非常古老的问题，但有新的方法来思考组允许在某些情况下取得进展。特别是在相对双曲群和双曲群的特定类别，如自由环群等领域取得了很大进展。具体来说，会议将讨论庞加莱对偶群，当某些类群是3-流形的基本群时，群的准有限补全，群的表面子群，以及类似于3-流形分解的群的分解。主要目标是通过将个人聚集在一起来获得具体的结果。有一个不断更新的会议网站：https://walsh-paoluzzi.weebly.com/conference.html。特别是，感兴趣的参与者可以在该网站预注册。

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.