Conference on Exotic Continua in Modern Mathematics

University Of Tennessee Knoxville, Knoxville TN

Investigators

Abstract

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.