Conference on Exotic Continua in Modern Mathematics

该奖项为参加将于2022年6月9日至12日在诺克斯维尔田纳西大学举行的第51届约翰和丽达·巴雷特纪念讲座的参与者，特别是学生和早期职业研究人员提供支持。这个为期四天的会议汇集了来自“奇异”连续体自然出现的四个数学领域的研究人员：(1)度量空间的分析，(2)奇异空间的几何，(3)拓扑动力系统，(4)几何群论。会议将为每个领域的研究人员提供一个机会，以获得对所有其他领域的广泛介绍，然后是更专门的会谈。会议的目标是找出方法上的共同点，并在这些领域之间产生交叉施肥。全体会议的讲师Judy Kennedy（一般连续体理论）、Nageswari Shanmugalingam（度量空间分析）、Guofang Wei（奇异空间几何）、Olga Lukina（拓扑动力系统）和Kim Ruane（几何群论）都是各自领域的杰出女性。全体会议发言人将参与就更专门的议题邀请其他发言人。会议鼓励年轻科学家和STEM中代表性不足的群体成员的包容和参与。连续体理论在数学中有着很长的历史，可以追溯到拓扑学成为一个独立领域的早期。连续空间被定义为连通的、紧致的、可度量的空间，包括“好”空间，如紧致流形。没有（或不知道）具有传统通用覆盖空间的可度量连续体被称为“外来的”。在寻找有趣的例子的过程中，奇异的连续体在我们现在所遇到的自然环境中出现之前就出现了。分形是应用分析中出现的重要问题的基础空间，例如在手机天线的设计中。分形是Peano连续体的一个例子，它包含了格罗莫夫-豪斯多夫意义上测地线空间的所有紧极限。奇异的连续体也出现在几何群论中，作为群和空间的边界，作为螺线空间，通过覆盖更好的空间（包括流形）的映射来推广被定义为逆极限的原始例子，但它们本身不需要是路径连接的。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 support for participants, especially students and early-career researchers, attending the 51st John and Lida Barrett Memorial Lectures which will be held on June 9-12, 2022, at University of Tennessee, Knoxville. This four-day conference brings together researchers from four areas of mathematics in which “exotic” continua naturally appear: (1) analysis on metric spaces, (2) geometry of singular spaces, (3) topological dynamical systems, and (4) geometric group theory. The conference will provide an opportunity for researchers in each area to obtain a broad introduction to all other areas, followed by more specialized talks. The goal of the conference is to bring out commonalities in methods and produce cross-fertilization between these areas. The plenary lecturers, Judy Kennedy (general continua theory), Nageswari Shanmugalingam (analysis on metric spaces), Guofang Wei (geometry of singular spaces), Olga Lukina (topological dynamical systems), and Kim Ruane (geometric group theory) are all prominent women in their respective areas. The plenary speakers will be involved in inviting additional speakers on more specialized topics. The conference encourages the inclusion and participation of junior scientists and members of groups under-represented in STEM.Continua theory has a very long history in mathematics, going back to the earliest days in which topology became a distinct field. Continua, which are defined as connected, compact, metrizable spaces, include “nice” spaces such as compact manifolds. Metrizable continua that do not (or are not known to) have a traditional universal covering space are referred as “exotic”. Exotic continua emerged in the quest for interesting examples long before they began to appear in the natural settings in which we now encounter them. Fractals appear as the underlying spaces that arise in important questions in analysis with applications, for example in design of cell phone antennae. Fractals are examples of Peano continua which in turn include all compact limits of geodesic spaces in the Gromov-Hausdorff sense. Exotic continua, also, arise as boundaries of groups and spaces in geometric group theory, and as solenoidal spaces, generalizing original examples that are defined as inverse limits via covering maps of much nicer spaces, including manifolds, but which themselves need not be path connected. The conference website is https://math.utk.edu/barrett/51st-lectures/.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.