Conference on Exotic Continua in Modern Mathematics

该奖项为参与者，特别是学生和早期职业研究人员提供支持，参加将于2022年6月9日至12日在田纳西大学诺克斯维尔举行的第51届约翰和利达巴雷特纪念讲座。这个为期四天的会议汇集了来自四个数学领域的研究人员，其中“异国情调”连续自然出现：（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，然后进行更专业的会谈。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相互促进作用。全体讲师，朱迪肯尼迪（一般连续理论），纳格斯瓦里Shanmugalingam（分析度量空间），Guofang魏（几何奇异空间），奥尔加Lukina（拓扑动力系统），和金Ruane（几何群论）都是突出的妇女在各自的领域。全体会议的发言者将参与邀请更多的发言者就更专门的议题发言。会议鼓励年轻科学家和在STEM中代表性不足的团体成员的包容和参与。连续统理论在数学中有着非常悠久的历史，可以追溯到拓扑学成为一个独特领域的最早时期。连续统，被定义为连通的，紧的，可度量的空间，包括“好”的空间，如紧流形。没有（或不知道）传统的泛覆盖空间的可度量化连续统被称为“奇异”。奇异的连续统出现在寻找有趣的例子的过程中，早在它们开始出现在我们现在遇到的自然环境中之前。分形作为潜在的空间出现在分析和应用中的重要问题中，例如在手机天线的设计中。分形是皮亚诺连续统的例子，皮亚诺连续统又包括Gromov-Hausdorff意义下测地线空间的所有紧极限。奇异连续统，也出现在几何群论中的群和空间的边界，以及作为螺线管空间，推广了最初的例子，这些例子通过覆盖更好的空间（包括流形）的映射被定义为逆极限，但它们本身不需要是路径连通的。会议网站是https://math.utk.edu/barrett/51st-lectures/.This奖反映了NSF的法定使命，并已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的支持。

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.