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届约翰和利达·巴雷特纪念讲座的参与者提供支持，特别是学生和职业生涯早期研究人员。这次为期四天的会议汇集了来自四个数学领域的研究人员，这些领域自然会出现“奇异”的连续性：(1)度量空间的分析，(2)奇异空间的几何，(3)拓扑动力系统，和(4)几何群论。会议将为每个领域的研究人员提供一个机会，对所有其他领域进行广泛的介绍，然后进行更专门的演讲。会议的目标是在方法上找到共同点，并在这些领域之间产生互惠互利。全体讲师朱迪·肯尼迪(一般连续体论)、Nageswari Shanmugalingam(度量空间分析)、郭方伟(奇异空间几何)、Olga Luina(拓扑动力系统)和Kim Ruane(几何群论)都是各自领域的杰出女性。全体发言者将参与邀请更多的发言者就更专门的主题发言。会议鼓励初级科学家和STEM中代表不足的群体的成员加入和参与。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早期。连续体被定义为连通的、紧致的、可度量的空间，包括紧致流形之类的“好”空间。没有(或不知道)有传统的普适覆盖空间的可度量化连续体被称为“奇异”。在寻找有趣的例子的过程中，异国情调的延续出现了很久，早在它们开始出现在我们现在遇到它们的自然环境之前。在应用分析的重要问题中，例如在手机天线的设计中，分形图作为底层空间出现。分形是Peano连续体的例子，而Peano连续体又包括Gromov-Hausdorff意义下测地线空间的所有紧极限。奇异连续体也作为几何群论中的群和空间的边界以及螺线空间出现，通过覆盖更好的空间(包括流形)的映射来推广原始例子，这些例子被定义为逆极限，但它们本身不需要是路径连接的。会议网站是https://math.utk.edu/barrett/51st-lectures/.This奖，反映了国家科学基金会的法定使命，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 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.