Conference: Cornell Topology

该奖项是为了支持康奈尔拓扑节的几次会议的演讲者和参与者，康奈尔拓扑节是康奈尔大学的年度会议，计划于2023年5月5日至7日举行。自1963年以来，该会议一直是美国东北部拓扑学家和几何学家数学生活中的一股力量，为发展和传播代数、微分和几何拓扑学及其相关学科的广泛结果提供了一个舞台。这些活动旨在鼓励拓扑学不同分支之间的数学广度和思想交流，以及欢迎早期职业数学家进入该领域，并促进初级和高级参与者之间的互动。每年，几次讲座都围绕一个重要的主题，以便向其他地区的拓扑学家传达一个分区的最新研究进展，并就最近感兴趣的主题教育研究生和早期职业研究人员。会议的每一次迭代都以初级初级演讲者为期一天的介绍性演讲开始，并就选定为主题的主题的历史进行座谈。它还包括一段关于激动人心的新研究方向的闪电般的简短演讲。所有这些活动都是为了应对最近日益专业化的趋势，在可获得的水平上展示相互关联的领域的发展情况。2023年会议感兴趣的领域将是4-流形理论的最新发展，这是一个与几何、代数和辛拓扑与几何有着深刻联系的话题。大约三分之一的讲座将围绕这一主题，以便向跨子学科的拓扑学家介绍这一领域比参加单一讲座或小型课程所能获得的更详细的内容。未来可能的主题包括：高维负曲线流形、迹方法和同伦类型理论；尽管组织者仍然灵活，如果在其他地方出现新的令人兴奋的发展。会议的其余部分展示了从广度角度选择的拓扑学不同领域的广泛最新发展。此外，所有演讲者都会参加一个“闪电回合”，其中包括其他人最近令人兴奋的工作的简短介绍和对未来趋势的猜测。这为新的发展提供了前瞻性的视角，并激发了讨论。活动和研究生讲座的开始介绍日为感兴趣的非专家提供了一个切入点，并鼓励研究生参与。这些活动的更广泛的影响包括：一个训练有素的拓扑学家群体，能够超越分专业的界限；一个更加多样化的数学工作队伍；更快地将年轻的拓扑学家融入当前的研究领域；以及加强不同拓扑学领域的研究人员之间的合作。会议的培训效果将通过分发研讨会的讲稿以及小组讨论和问题会议的摘要来扩大；会议的主要工具是会议网站，自从1997.https://e.math.cornell.edu/sites/topology/This奖反映了国家科学基金会的法定使命以来，该网站一直得到维护，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award is to support speakers and participants at several meetings of the Cornell Topology Festival, an annual conference at Cornell University, starting with the conference planned for May 5-7, 2023. The conference has been a force in the mathematical life of topologists and geometers in the northeastern United States since 1963, providing an arena for the development and dissemination of a broad array of results from within algebraic, differential, and geometric topology and allied subjects. The activities are designed to encourage mathematical breadth and exchange of ideas between different branches of topology, as well as to welcome early career mathematicians into the field and promote interactions between junior and senior participants. Each year, several of the talks cluster around one significant theme, in order to communicated a recent research development in one subarea to topologists across other areas, and to educate graduate students and early career researchers on a subject of recent interest. Each iteration of the conference starts with a day of introductory talks by early junior speakers, and a colloquium talk on the history of the topic chosen for the main theme. It also includes a lightning session of short talks on exciting new research directions. All of these activities serve to counter recent trends towards increasing specialization, by showcasing developments across inter-related fields at an accessible level. The area of interest for the 2023 conference will be recent developments in the theory of 4-manifolds, a topic with deep connections to geometric, algebraic, and symplectic topology and geometry. About one third of the talks will be on this subject, in order to introduce topologists across sub-disciplines to this area in more detail than obtainable by attending a single talk or mini-course. Possible future themes include: high dimensional negatively curved manifolds, trace methods, and homotopy type theory; although the organizers remain flexible should a new exciting development come to light elsewhere. The remainder of talks at the conference showcase a broad range of recent developments in different areas of topology, selected with a view towards breadth. Additionally, all speakers participate in a “lightning round” consisting of short pitches of recent exciting work by others and speculation on future trends. This gives a forward-looking perspective on new developments and stimulates discussion. The opening introductory day of activities and graduate student talks provides a point of entry for interested non-experts and encourages graduate student involvement. The broader impacts of the activities include a more broadly-trained community of topologists, able to transcend the boundaries of subspecialties; a more diverse mathematical workforce; a more rapid integration of younger topologists into areas of current research; and the enhancement of collaboration among researchers in different areas of topology. The training effects of the conference will be extended by dissemination of lecture notes from the workshops and summaries of the panel discussion and problem session; the main vehicle for this is the conference web site, which has been maintained continuously since 1997.https://e.math.cornell.edu/sites/topology/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.