Conference: St. Louis Topology Conference: Flows and Foliations in 3-Manifolds

该奖项为2024年5月17日至19日在美国密苏里州圣路易斯举行的圣路易斯拓扑会议提供参与者支持。会议的主题是3流形中的流和叶。动力系统的数学概念允许在一个统一的框架内考虑任何连续时变的物理系统，作为组织所有可能的瞬时配置的“状态空间”，以及描述状态随时间演变的“流”。会议的重点是空间的几何和拓扑与它所支持的各种动态系统相互作用的方式，并着眼于在动力学，几何和拓扑中的应用。组织者致力于广泛招募各种各样的学生和博士后研究人员。除了由知名研究人员进行的长达一小时的讲座外，还将有闪电演讲以及关于早期职业数学家面临的问题的小组讨论。三维流形中的流动和叶状可以通过许多镜头进行富有成效的观察，因为它们处于动力学，拓扑和几何的交叉点。自从Agol解决了虚拟纤维猜想以来，对这一领域的兴趣加速了，研究人员使用各种工具和思想，如（伪）ansov和部分双曲流，缝合流形层次，几何群论，接触几何，Floer理论，转向三角测量，以及所谓的大映射类群来研究各种问题。其中包括l空间猜想，Cannon猜想，伪anosov有限猜想，以及无限型映射类的分类。最近的会议倾向于关注这些主题和技术的一小部分，因此需要一个活动，使具有这些不同主题专业知识的研究人员能够会面并分享他们的知识。会谈将在华盛顿大学举行。该奖项反映了NSF的法定使命，并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，认为值得支持。

This award provides participant support for the St. Louis Topology Conference taking place May 17-19, 2024 in St. Louis, Missouri, USA. The theme of the conference is Flows and Foliations in 3-manifolds. The mathematical concept of a dynamical system allows for any continuously time-varying physical system to be considered within a uniform framework, as a “state space” that organizes all possible instantaneous configurations, together with a “flow” that describes the evolution of states with time. The conference is focused on the way that the geometry and topology of a space interacts with the kinds of dynamical systems that it supports, with an eye towards applications in dynamics, geometry, and topology. The organizers are committed to broad recruitment across a diverse set of students and postdoctoral researchers. In addition to hour-long lectures by established researchers, there will be lightning talks as well as a panel discussion on issues faced by early career mathematicians.Flows and foliations in three dimensional manifolds can be fruitfully viewed through many lenses, as they stand at the intersection of dynamics, topology, and geometry. Interest in this general area has accelerated since Agol's resolution of the Virtual Fibering Conjecture, with researchers using a variety of tools and ideas such as (pseudo-) Anosov and partially hyperbolic flows, sutured manifold hierarchies, geometric group theory, contact geometry, Floer theory, veering triangulations, and the so-called big mapping class group to study a variety of questions. These include among others the L-space conjecture, the Cannon Conjecture, the Pseudo-Anosov Finiteness Conjecture, and the classification of infinite-type mapping classes. Recent conferences have tended to focus on small subsets of these topics and techniques, and there is a need for an event at which researchers with expertise in these different topics can meet and share their knowledge. Talks will take place at Washington University. The conference website is https://sites.google.com/view/stltc/home.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.