Collaborative Research: Conference: Trisections Workshops: Connections with Knotted Surfaces and Diffeomorphisms

该提案将资助“三等分研讨会：与打结表面的连接”，这将于2024年6月24日至28日在内布拉斯加大学林肯分校举行，以及“三等分研讨会：与非同构的连接”，这将于2025年夏天在德克萨斯大学奥斯汀分校举行。 研讨会的与会者将包括知名专家，早期职业研究人员和学生，该计划将积极吸引所有参与者。 每天上午将举行专家全体会议和/或闪电会谈，突出初级研究人员的工作。 下午将用于分组讨论未决问题。 这一系列的定期研讨会对于低维拓扑研究人员的热情社区的发展至关重要，帮助这个新的和不断增长的领域获得动力，并促进跨职业阶段和人口统计的众多合作。组织者为他们努力创造的同志情谊和热情的氛围感到自豪，社区中的许多人都非常重视和欣赏这些活动。 三分法将一个四维空间分成三个简单的部分。 自从大约十年前引入以来，三分性已经被证明是研究光滑4-流形的成功的新工具，在此期间写了许多文章来发展三分性理论的基础。三分理论的一个重要优势是它与低维拓扑中的各种其他主题的接口方式。 这个接口提供了一个机会，通过一个新的透镜，探索许多经典领域的4-流形拓扑结构。这些领域包括，例如，研究打结的表面在4空间，仿射的4流形，异国情调的光滑结构，群作用和（分支）覆盖空间，和辛结构。 这些研讨会的主要目标是汇集来自多个领域的研究人员，提出并解决开放性问题，特别关注早期职业研究人员的参与。 在讲习班之前，将举行一系列虚拟的讲习班前介绍性谈话，使新的研究人员跟上进度，便利小组开展工作，并吸收世界各地更广泛的听众。 2024年研讨会的网站可以在这里找到：https://sites.google.com/view/tw2024.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

This proposal will fund the “Trisections Workshop: Connections with Knotted Surfaces,” which will take place at the University of Nebraska-Lincoln from June 24-28, 2024, and the “Trisections Workshop: Connections with Diffeomorphisms,” which will take place at the University of Texas at Austin during one week in the summer of 2025. Workshop attendees will include established experts, early-career researchers, and students, and the program will actively engage all participants. Each morning will feature plenary talks by experts and/or lightning talks highlighting the work of junior researchers. The afternoons will be devoted to working in groups on open problems. This series of regular workshops has been critical to the development of an enthusiastic community of researchers in low-dimensional topology, helping this new and growing area gain momentum and fostering numerous collaborations across career stages and demographics. The organizers take pride in the camaraderie and welcoming atmosphere they strive to create, and many in the community deeply value and appreciate these events. A trisection splits a 4-dimensional space into three simple pieces. Since their introduction roughly a decade ago, trisections have proven to be a successful new tool with which to study smooth 4-manifolds, with numerous articles written in the interim to develop the foundations for trisection theory. An important strength of the theory of trisections is the way it interfaces with a variety of other topics in low-dimensional topology. This interface provides an opportunity to explore many classical areas of 4-manifold topology through a new lens. Such areas include, for example, the study of knotted surfaces in 4-space, diffeomorphisms of 4-manifolds, exotic smooth structures, group actions and (branched) covering spaces, and symplectic structures. The main goal of these workshops is to bring together researchers from multiple areas to propose and to work on open problems, with a particular focus on the inclusion of early career researchers. The workshops are preceded by a series of introductory virtual pre-workshop talks, which serve to bring new researchers up to speed, to facilitate the work to be done in groups, and to incorporate a broader, worldwide audience. The website for the 2024 workshop can be found here: https://sites.google.com/view/tw2024.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.